They probably hang them upside down as added dishonor to the fact that they weren't worthy enough to be considered a trophy kill. Or perhaps it's as a subliminal warning to those who do not meet expectations. As for why they're skinned in the first place? I'd just go with the principle of insult to injury- it's bad enough that the prey was killed and never fashioned into something worthwhile after the kill, but the lack of skin and organs makes them look like the way the Predator must envision them to be...weak and unworthy.
All presumption, but I have the feeling it's more out of ritual reasoning than anything else.