seankreynolds said:
<snipped references>
The above doesn't mention the movement of quarks and electrons (other than electrons being in their lowest ground state) ... so those subatomic particles are still moving in some way (for example, even in their lowest energy state, electrons are still moving at the speed of light), thus, energy. Theoretically, you could extract that energy (though in the real world we don't know how to do that) and thus make that material "colder," even if it's at absolute zero, but not in a sense meaningful to the use of the word "temperature."
OK, now I see where you were coming from. My degree is in Nuclear Engineering, so I spent a lot more time looking at subatomic particles than at whole atoms and molecules; that's probably why I came at this from a different slant. Here's how I would interpret the references you cited:
The references didn't mention the motions of subatomic particles because in almost all real-world cases they're not relevant--since, as you point out, we don't know any way of extracting whatever "extra" energy is still in them. However, if there is any way of extracting such energy from *any* particles in the system, whether it's nucleons in the nucleus or electrons orbiting the nucleus (I don't think they're moving at the speed of light in their lowest energy state to begin with--photons, yes, electrons no--but in any case if they're in their lowest energy state within the atom then by definition you can't extract any more energy from them), then the system isn't truly at absolute zero. The definition of absolute zero is that *no* further energy can be extracted at all, from any part of the system, by any process whatever.
If we don't yet know of a process to extract more energy from some system, we may *think* it's at absolute zero; but if we discover such a process in the future, that doesn't show that we can now cool something below absolute zero; it just shows we were wrong in thinking the system was at absolute zero before.
Edit: The following article in the Usenet Physics FAQ goes into more detail about the viewpoint I'm taking here; it gives a more general definition of temperature than "average kinetic energy of particles", which is the one you used, and explains how negative temperatures work.
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html
P. S.: Saw the press release for your new gaming company. Good luck! I look forward to taking a look at your products; if they're anything like the stuff already on your website I'll probably be a customer.