As far as testicular torsion goes, if that happens surgery is required immediately, otherwise the testicle will die. In any case, sleep attire has nothing to do with testicular torsion.
I asked my husband about supporting the testicles, and and he said that's silly. Most guys don't even wear jock straps anymore during basketball, etc. because they have proven unnecessary in most cases. Testicles don't need support, and certainly not while one sleeps. Testicles aren't heavy like stones, and they certainly don't swing around. My two sons just sleep in their boxers and have never complained about lack of support. That's absurd.