Temperature in this sense no longer has anything to do with kinetic energy. A quantum system at absolute zero would simply be in its ground state, which is perfectly possible. In open space you only run into problems that there's not a particularly clear minimum.

You do run into some problems with quantum fluctuations which may or may not randomly add energy to the system, I guess that's what this new result is about.

It seems to me that uncertainty is more uncertain a theorum to base your beliefs about the universe on than entropy.

True perhaps, but we're relatively certain about uncertainty.

Basing it on entropy makes certain assumptions on topological properties of time and space though.

Also, all the other particles in the universe will exert a force on the particle (through e.g. gravitation), which will probably result in (small) vibration of the the particle.