I don't know. Either things that people say they want are paramount, or not. Unless they are starving, people would say no to "used food" like a hamburger with a bite taken out of it too.
I suppose it depends if you are trying to help with people's wants or needs in a disaster situation. If 10 new sweatshirts and 100 used sweatshirts get airdropped into a disaster area, and all 10 new shirts get taken and 0 used shirts, then FEMA is right, cloths are not needed. However, if the cloths being new help people psychologically cope with the disaster, that's certainly a factor to consider.