Schwarzschild geometry in Schwarzschild coordinates $(t,r,\theta,\phi)$ is time-symmetric
\begin{equation}
ds^2=-\left(1-\frac{2GM}{c^2 r}\right)c^2dt^2+\left(1-\frac{2GM}{c^2 r}\right)^{-1}dr^2+r^2\left(d \theta^2 +\sin^2 \theta d \phi^2\right) \;.
\end{equation}
Novikov coordinate system is defined by a set of geodesic clocks. The coordinate clocks are freely falling from some maximal radius $r_m$ towards $r=0$, where $r_m$ is different for each clock. All clocks start falling at the same Schwarzschild time $t_0$ and they are synchronized in such a manner that each clock shows $0$ at $r_m$. Novikov coordinate is defined to stay constant along the trajectory of each clock, while for time coordinate proper time is taken.
From now on the angular part metric will be omitted, since is stays the same. We also take $r_s=2M$ and $G=c=1$:
\begin{equation}\label{eq:sch-met2}
ds^2=-\left(1-\frac{r_s}{r}\right)dt^2+\left(1-\frac{r_s}{r}\right)^{-1}dr^2 \;.
\end{equation}
Geodesics in Schwarzschild gometry
To get the equation of geodesics in Schwarzschild geometry we have to solve equations of motion of a free particle:
\begin{equation}\label{eq:lagrangian}
\mathcal{L}=\frac{1}{2}mg_{\mu\nu}\dot{x}^\mu\dot{x}^\nu \;,
\end{equation}
\begin{equation}\label{eq:dot}
\dot{x}^\mu=\frac{dx^\mu}{d\tau}=u^\mu \;.
\end{equation}
\begin{equation}\label{eq:lagrangian2}
\mathcal{L}=-\frac{m}{2}\left(1-\frac{r_s}{r}\right)\dot{t}^2+\left(1-\frac{r_s}{r}\right)^{-1}\dot{r}^2 \;,
\end{equation}
\begin{equation}\label{eq:EL}
\frac{d}{d\tau}\frac{\partial\mathcal{L}}{\partial \dot{x}^\mu}-\frac{\partial\mathcal{L}}{\partial x^\mu}=0 \;,
\end{equation}
For $\mu=0$ we get a constant of motion
\begin{equation}\label{eq:ConstOfMotion}
\frac{\partial}{\partial\tau}\left[\left(1-\frac{r_s}{r}\right)\dot{t}\right]=0 \qquad \Rightarrow \qquad \left(1-\frac{r_s}{r}\right)\dot{t}=a \;,
\end{equation}
For timelike geodesics: $ds^2=-d\tau^2$ the radial geodesic equation becomes
\begin{equation}\label{eq:orbit}
\left(\frac{d\tau}{dr}\right)^2=\frac{1}{a^2-\left(1-\frac{r_s}{r}\right)} \;.
\end{equation}
Maximal radius is ($dr/d\tau=0$)
\begin{equation}\label{eq:maximal}
r_m=\frac{r_s}{1-a^2} \;.
\end{equation}
We use $\frac{dt}{dr}=\frac{dt}{d\tau}\frac{d\tau}{dr}$ and obtain the following relations:
\begin{eqnarray}
\frac{d\tau}{dr} &=& \frac{\varepsilon}{\sqrt{\frac{r_s}{r}-\frac{r_s}{r_m}}} \;,\label{eq:orbit1} \
\frac{dt}{dr} &=& \frac{\varepsilon\sqrt{1-\frac{r_s}{r_m}}}{\left(1-\frac{r_s}{r}\right)\sqrt{\frac{r_s}{r}-\frac{r_s}{r_m}}} \;, \label{eq:orbit2}
\end{eqnarray}
where $\varepsilon$ is $+1$ or $-1$. For falling particles we choose $\varepsilon=-1$.
Novikov time coordinate
We first transform from $(r,t)$ to $(r,\tau)$.
From last two equations we obtain for $d\tau(dt,dr)$
\begin{equation}\label{eq:bit}
d\tau=\left(1-\frac{r_s}{r_m}\right)^{1/2}dt+\frac{\left(\frac{r_s}{r}-\frac{r_s}{r_m}\right)^{1/2}}{1-\frac{r_s}{r}}dr \;.
\end{equation}
where we assumed $t$ are $r$ known.
This can be integratet from $r$ to $r_m$, where we take into account that all clocks reach their maximum radius at $\tau_{0i}=0$. It follows
\begin{equation}\label{eq:integral}
\tau=\left(1-\frac{r_s}{r_m}\right)^{1/2}(t-t_0)+\int_{r_m}^{r}\frac{\left(\frac{r_s}{y}-\frac{r_s}{r_m}\right)^{1/2}}{1-\frac{r_s}{y}}dy \;.
\end{equation}
maximal radius $r_m$ is here a function of $r$ and \tau$. Their implicit relationship is
\begin{equation}\label{eq:implicit1}
\tau=-f(r,r_m)\;,
\end{equation}
where
\begin{equation}
f(r,r_m) = \int_{r_m}^{r}\frac{dy}{\sqrt{\frac{r_s}{y}-\frac{r_s}{r_m}}} \label{eq:integral3}
= -\left[\frac{rr_m}{r_s}(r_m-r)\right]^{1/2}-\frac{r_m^{3/2}}{\sqrt{r_s}}\arccos\left[\left(\frac{r}{r_m}\right)^{1/2}\right] \;.\label{eq:f}
\end{equation}
We can now eliminate coordinate $t$ from the line element
\begin{equation}\label{eq:sch-met3}
ds^2=-d\tau^2+\frac{1}{1-\frac{r_s}{r_m}}\left[- dr-\left(\frac{r_s}{r}-\frac{r_s}{r_m}\right)^{1/2}d\tau\right]^2 \;.
\end{equation}
Novikov radial coordinate
For radial coordinate we take the maximal Schwarzschild radius $r_m$, which remains constant along the worldline of a geodesic clock.
\begin{equation}\label{eq:relation2}
- dr-\left(\frac{r_s}{r}-\frac{r_s}{r_m}\right)^{1/2}d\tau=\left(\frac{r_s}{r}-\frac{r_s}{r_m}\right)^{1/2}\frac{\partial f}{\partial r_m}dr_m \;.
\end{equation}
With this we can eliminate the other Schwrazschild coordinate $r$:
\begin{equation}\label{eq:sch-met4}
ds^2=-d\tau^2+\frac{\left[g(r,r_m)\right]^2}{1-\frac{r_s}{r_m}}dr_m^2 \;.
\end{equation}
Here we $g(r,r_m)$ is the following
\begin{eqnarray}
g(r,r_m)&=&-\left(\frac{r_s}{r}-\frac{r_s}{r_m}\right)^{1/2}\frac{\partial f}{\partial r_m} \label{eq:g}\
&=&1+\frac{1}{2}\left(1-\frac{r}{r_m}\right)-\frac{3}{4}\left(\frac{r_m}{r}-1\right)^{1/2}\left[\sin^{-1}\left(\frac{2r}{r_m}-1\right)-\frac{\pi}{2}\right] \;. \nonumber
\end{eqnarray}
$r$ is not a radial coordinate anymore, but a metric function of coordinates $r_m$ and $\tau$, which is given implicitly by equation ().
Novikov metric
By introducting $r_m$ the metric became diagonal as in Schwarzschild coordinates. It also stays diagonal by introducig a new radial coordinate, that is only functionally related to the old one. Novikov-s choice is $r^*$ with the following monotonic relation to $r_m$:
\begin{equation}\label{eq:r*}
r^*=\left(\frac{r_m}{r_s}-1\right)^{1/2}\;.
\end{equation}
The metric now becomes
\begin{equation}\label{eq:novikov-met}
ds^2=-d\tau^2+4r_s^2\left({r^*}^2+1\right)\left[g(r,r^*)\right]^2d{r^*}^2 \;.
\end{equation}
We can show that the following also holds
\begin{equation}\label{eq:relation}
4Mg(r,r^*)=\frac{1}{r^*}\frac{\partial r}{\partial r^*}\;.
\end{equation}
With this the metric gets the form that is standard in literature [MTW,p. 826]:
\begin{equation}\label{eq:novikov}
ds^2=-d\tau^2+\left(\frac{{r^*}^2+1}{{r^*}^2}\right)\left(\frac{\partial r}{\partial r^*}\right)^2d{r^*}^2+r^2\left(d \theta^2 +\sin^2 \theta d \phi^2\right) \;,
\end{equation}
where we also included the angular part.
Relations among coordinates
We now give the relations between Schwarzschild coordinates $(t,r)$ and Novikov coordinates $(\tau,r^*)$. The first one, $r=(\tau,r^*)$, is obtained from equations () and ()
\begin{equation}\label{eq:CoordRela1}
\tau=r_s\left({r^*}^2+1\right)\left[\frac{r}{r_s}-\frac{(r/r_s)^2}{{r^*}^2+1}\right]^{1/2}+r_s\left({r^*}^2+1\right)^{3/2}\arccos\left[\left(\frac{r/r_s}{{r^*}^2+1}\right)^{1/2}\right] \;.
\end{equation}
The second one, $t=(\tau,r^*)$, is obtained by integration from ()
\begin{equation}
t=r_s\ln\left|\frac{r^*+\left(\frac{r_s}{r}\left({r^}^2+1\right)-1\right)^{1/2}}{r^-\left(\frac{r_s}{r}\left({r^*}^2+1\right)-1\right)^{1/2}}\right|+r_sr^\left[\left({r^}^2+3\right)\arctan\left(\frac{r_s}{r}\left({r^}^2+1\right)-1\right)^{1/2}+\left({r^}^2+1\right)\frac{\sqrt{\frac{r_s}{r}\left({r^*}^2+1\right)-1}}{\frac{r_s}{r}\left({r^*}^2+1\right)}\right] \;.
\end{equation}
Best Answer
In short, that is a way of saying it. However, it should be taken with a grain of salt: no one is saying that you can find a stress-energy tensor for the gravitational field itself. Think of it as an intuitive view.
Pick a Schwarzschild black hole, for example. It is a vacuum solution of the Einstein Field Equations, so there is no matter anywhere in spacetime to bend spacetime. Yet, it is bent. Furthermore, if we compute the mass of the spacetime (for example, the ADM mass), we'll find a non-vanishing value. A convenient way of understanding this is that it is as if there was gravitational energy sourcing this bending. Notice I'm not saying there is a gravitational stress-energy tensor nor giving a coordinate-invariant, local definition of gravitational energy. Rather, I'm saying this is a way of interpreting in an intuitive manner what is going on.
Similarly, one can do this things to interpret, for example, redshifts. In a black hole, it is common to understand the redshift of a photon as it "climbs" out of the potential well: the photon loses energy to the gravitational field and is redshifted as a result, and we state is as if the gravitational field was gaining energy even though it does not have a stress-energy tensor.
Another example is with an expanding Universe. In Cosmology, energy is not generally conserved. However, there is a way of interpreting the equations of General Relativity and keep energy constant at cosmological scales: add on gravitational energy. This is comfortable because it allows us to interpret things in terms of constant total energy, but uncomfortable because gravity does not have a stress-energy tensor, and so on. Sean Carroll mentions it in one of his blog posts.
As a summary, Thorne is nowhere stating that there is a local, coordinate-independent notion of gravitational energy. The point is that it is sometime convenient to understand the nonlinear effects of General Relativity as being due to some sort of gravitational energy. To be fair, one can derive the Einstein–Hilbert action in this way (see e.g., Zee's Einstein Gravity in a Nutshell, Chap. IX.5 if I recall correctly).