The two black holes observed by LIGO were around 30 solar masses each - they were formed from stellar sources - that is, a supernova or similar event. They are not the same "kind" of black holes which are found in the middle of galaxies.
(sidenote: The fact that they are 30 solar masses is actually interesting. In this paper they discuss how the environment had to be a little bit special for these black holes to form).
In regards to the condition of "truth", it conforms to established scientific norms. For instance, the detector has been very well-modeled and every reasonable error has been accounted for, so we have very good reason to believe that the signal is real (to say nothing about the fact that it was observed in TWO detectors, one in Louisiana and one in Washington, and the signals are nearly identical). To determine the details of the merger, people have been working very hard over the past decade to develop a library of signals, for a variety of objects (neutron stars and black holes) and a wide variety of parameters (masses and orbital parameters). So they determined the characteristics of the merger by comparison with those models.
Of course, we aren't in a spaceship floating over this merger viewing it with our own eyes. But on the basis of the scientific method (hypothesis testing and independent verification), this establishes the existence of gravitational waves.
(for the full paper talking about the observation)
EDIT: I'm going to try to tackle your clarifying questions.
This one is slightly tricky, since all (extra-solar) astronomy is indirect in this way - we only observe the cosmos via the light we receive from it. For example, the existence of the star Polaris is indirect, and depends on the assumption that stars produce light (which is on very solid footing, obviously). Some examples that might be closer to what you're thinking of - Dark matter is only detected via it's gravitational influence (never directly), but most people consider it to be a real phenomena. Pulsars being associated to neutron stars is mostly theoretical - although we can associate them to SNR sometimes. And actually, the vast majority of extrasolar planets are detected indirectly, via the Doppler shift or transit methods.
I think the answer is "no". You would have to explore each one individually, since the argument in each case is rather unique. I once listened to an interesting podcast about how astronomy is observational, not experimental. I think it's here. I think the best you can do is list evidence for discovery and let the community decide. This is not a unique problem, BTW - no one has ever seen a Higgs particle, in the traditional sense - we inferred it's existence at a level sufficient for the scientific community.
LIGO releases it's data to the public at proscribed times. Here's a list of projects using LIGO data. I don't think I see specifically what you are interested in ("We checked LIGO, it's right!"), but this list is only the past few months.
This represents a major misunderstanding of what a gravitational wave is. The effect presented is simply the semi-static gravitational field at earth due to the earth, moon and sun. It is predicted by Newtonian gravity. There is no 'wave' that propagated, it's the instant positions of the 3 bodies that change over 1 day (and over 1 year also).
It does not show that the change moved at the speed of light, which gravitational waves do. Nothing in Newton's equations talk about the speed of light. The GR equations for 3 bodies moving like the earth-sun-moon can only be solved approximately, and in this case it'd be through a post-Newtonian approximation. The pseudo-static term(s) would be the same but possibly some GR correction - and if it is (And I'm not sure if the strongest term correction might not be something like the term for the perihelion of mercury, or something else, in any case extremely small and not measurable in their g measurement). But that's not even a grav wave. The grav waves would be even smaller probably - you'd have to compute the rate of change of the quadrupole moment of the configuration, and do some other calculations. The simpler problem of just the grav radiation of the earth-sun rotation around each other gives a resultant power dissipated that translates in the orbit of the earth loosing altitude ('altitude' above the sun) of the size of 1 proton per day. That g change they measured in your graph is about 10 to the minus 7 g's. It isn't even dissipative, as the bodies keep doing the same thing over and over, in your approximation. If you don't see that dissipation you are not seeing the gravitational waves.
There is probably many other ways to see that what you're discussing, what the graphic measured, is not a gravitational wave, but rather a very slow change in a static gravity field, the one produced by the 3 bodies.
Grav waves produce something different than just a change in gravity in one direction, they do it in 2 directions at once, an asymmetrical squeezing of a circle first in one axis and then in the other, like squeezing a balloon in one direction, making it bulge in the other.
Like Nathaniel said, it's like comparing a (semi) static electric field (say produced by rubbing a couple rags together) and moving them around some, with light.
Note: yes, even changing static fields can not produce a change in what's observed at a distance faster than the speed of light, but that doesn't come in at all in your graphic, too small a differential effect for it to see it.
Best Answer
The strain (ratio of displacement from equilibrium to equilibrium separation) of gravitational waves decreases as $1/r$ for a distance $r$ from the source. Since the strain in this case peaked at $10^{-21}$ at a distance of $1.3\times10^9\ \mathrm{ly} = 1.3\times10^{25}\ \mathrm{m}$, you would expect strains on the order of $1\%$ at a distance of $1300\ \mathrm{km}$. For reference, the observed signal is from black holes that were about $100\ \mathrm{km}$ in radius initially.
Much closer than this, and the linearized theory of GR breaks down. Gravitational waves are only well-defined in the small-amplitude limit. Close-in, we have the near-field regime where nonlinear effects that can't really be described as simple waves dominate. The only simple statement that really can be made here is that distortions are even stronger closer in.