Exactly- getting gun shot residue on her hands may have been something he wanted. I'll just bet he probably didn't even shoot himself, just let her do it, and I'll bet he wore gloves to keep his hands clean.
Still, though, what's even more intriguing is the missing bullet from Krystal's friend's gun. It would make more sense if they were going to set up a suicide using Kelsey's gun, but possibly using her friend's gun? We don't know that they did that, nor do we know officially if they fired that gun, but it sure is strange that the friend brought that up, that she even noticed a bullet was missing.
I wonder, was Kelsey's gun the same as her friend's gun? Could Kelsey's gun have been empty of bullets, Patrick forgot to get more or didn't have any more around, and they took one from her friend's gun, to put into Kelsey's gun to shoot her with?