I didn't read every post in the thread, but what some people here seem to be missing is the fact that infinite mechanical rigidity doesn't mean that Lorentz (relativistic) contraction cannot occur.
In mechanical compression the molecules come closer together by moving relative to each other. Infinite mechanical rigidity would mean the molecules can't move relative to each other and so the intermolecular distance can't be altered.
In relativistic contraction, the
very notion of length changes according to the reference frame. That is, the molecules (and intermolecular distances, and everything else in motion) themselves become shorter for the observer. Also, different observers can have different length measurements for the same thing.
So, while something can be immune to mechanical compression, it can't be immune to relativistic contraction, which just happens (no force involved or anything, it's just a law of the universe).
See Ehrenfest Paradox:
http://en.wikipedia.org/wiki/Ehrenfest_paradox