Short answer: Yes, I'd buy the Berkeley group's work; their value of $\mu$ is the highest I've seen...
Long answer: Yes. The question arises because of widespread confusion between the terms "adhesion" and "friction".
Crudely, adhesion is a force that resists the separation of in-contact surfaces in the normal direction. Friction is a force that opposes relative tangential motion between two in-contact surfaces. One need not imply the other, their causative mechanisms are distinct and in fact most models exclusively address one or the other.
Adhesion is driven by Van der Waals kinda forces.
"Coulomb" friction (solid-solid) is caused by the presence of asperities (think small bumps or protrusions) on surfaces. Due to the presence of these asperities, the "real" area of contact between two surfaces is much smaller than the "apparent" area of contact.
The Coulomb model is a phenomenological fit to experiments that was shown to be deducible assuming this type of contact. In some sense this sets an upper bound on the resistance to the tangential relative motion between surfaces.
If you somehow ensure these areas are very nearly the same, would $\mu$ then increase?
There are, indeed, "intimate" contacts where the apparent and real areas of contact are very nearly the same and the resistance to sliding large. In such cases, the frictional behavior is intimately linked to the mechanisms of deformation at the small scale (e.g. plasticity in metals). However, even this is not enough to get the largest possible $\mu$.
For instance, the maximum shear stress resisting relative motion in metals is capped to a maximum value, beyond which it cannot increase.
(i.e.) Instead of
Shear stress = $\mu\times$ Normal stress ...(I)
You would've
Shear stress = min ($\tau_{max}$ , $\mu\times$ Normal stress) ...(Ia)
Equation (I) is simply Coulomb's law applied locally.
Q = $\mu N$ ...(II)
Now, if someone devised a contact / material system that produces very high $Q$ for a given $N$ in equation (II) in an experiment, they could claim that they had devised a material with high friction coefficient.
This is essentially what the Berkeley group seems to have done. As I said, this kind of thing is hard to do with metals - even if intimate contact is achieved (say, under a state of severe deformation), something like Eqn. (Ia) kicks in and prevents the shear resistance from rising further. Previously, therefore, people achieved high $\mu$ using compliant, soft materials, but these guys use a microfiber array to engineer a surface with high $\mu$.
Their main advances are
(1) High $\mu$ than reported in soft materials
(2) Allowing control of $\mu$ by controlling the fiber layout etc
(3) Achieving high $\mu$ in combination with low adhesion, which was not the case in softer materials. This is the kind of property combination you'd need for automobile tyre.
Coming to the Gecko paper, it has far more to do with adhesion that friction. The Gecko paper and the Berkeley friction paper have little to do with each other. Also, contrary to popular myth, the Gecko mechanism has nothing to do with "suction". See these papers in Nature - it is largely adhesion driven.
Adhesive force of a single gecko foot-hair
K Autumn, YA Liang, ST Hsieh, W Zesch, WP Chan… - Nature, 2000
Micro-fabricated adhesive mimicking gecko foot-hair
AK Geim, SV Dubonos, IV Grigorieva… - Nature materials, 2003
For physicists interested in these areas - I understand that tribology and solid mechanics are not taught in US physics departments - it might help to refer to standard texts on Tribology by Bowden and Tabor, Kendall, Israelachvili, Persson, Maugis etc.
Or better still, talk to your colleagues who work in tribology (they're usually to be found in mechanical engineering, materials science and chemistry). They will be eager and willing to help, if only for the opportunity to brag at faculty meetings that a physicist asked them for advice :-)
I don't know of any research to find out if skin sunburns faster when wet, though someone did a comparable experiment to find out if plants can be burnt by sunlight focussed through drops of water after the plants have been watered.
You need to be clear what is being measured here. The total amount of sunlight hitting you, and a plant, is unaffected by whether you're wet or not. The question is whether water droplets can focus the sunlight onto intense patches causing small local burns.
The answer is that under most circumstances water droplets do not cause burning because unless the contact angle is very high they do not focus the sunlight onto the skin. Burning (of the plants) could happen if the droplets were held above the leaf surface by hairs, or when the water droplets were replaced by glass spheres (with an effective contact angle of 180º).
My observation of water droplets on my own skin is that the contact angles are less than 90º, so from the plant experiments these droplets would not cause local burning. The answer to your question is (probably) that wet skin does not burn faster. I would agree with Will that the cooling effect of water on the skin may make you unaware that you're being burnt, and this may lead to the common belief that wet skin accelerates burning.
Best Answer
Part of the explanation lies in the composition of the epidermis (outer skin), which is made up of mainly keratin. Hair, nails, animal horn and hooves are also made of this material.
Keratin has the peculiar property of softening when wet. This is due to some of the chemical bonds (that keep the keratin protein strands together) breaking in the presence of water. This causes loss of hardness, as experienced also when wetting hair of soaking finger or toe nails.
Softer materials usually show higher coefficients of friction (due to better 'grip'), compare e.g. soft silicone rubber to hard plastics or soft, malleable metals like lead to hard, rigid ones like stainless steel.