The parents both did. The father said he wasn't even there - said he was at Walmart, yet he mysteriously was tested positive for gunshot residue. And the mother had gunshot residue on her hands, not on her leg, where she was shot.
It's possible that if the woman held her hands up in an (obviously useless from any perspective) effort to defend herself from a gunshot she could have gotten residue on her hands.
Gunshot residue "sprays" from the bbl rather than "streams" and the patern expands the greater the distance from the bbl to surface upon which gunshot residue may reside.
The father could have gotten gunshot residue on his hands as a result of it being transfered there from the mother's hands.
We'd have to know when the parents' hands were tested for GSR, whether or not they had time to hold hands or touch hands prior to their being tested, and what the patern/location of GSR on both/either of their hands looked like at the time they were tested to even begin to speculate as to what the GSR might mean.
I suspect that the police have such information and that if things didn't line up in a manner that made it pretty clear that they were "victims" of gunshot residue (as opposed to suspects of GSR) they'd be under arrest at this time, or at least under investigation, and it's my understanding that neither is the case.
As to why the suspect didn't have GSR on his hands, he prolly washed them.
GSR isn't really permanent or "sticky" and it doesn't really "embed" itself in the skin (though it can be more difficult to remove from an open wound than from "health" skin). It's really more like metalic "dust" than anything else. It'll come off with a couple thorough washings with soap and water and for good measure you can kneed a ball of parafin wax for a while to pick up stray particles.
I don't know how long it was between the time the alleged shooting occured and the eventual arrest but if there was time for him to wash his hands in the interim that could certainly explain it.
GSR is more kinda "circumstantial" evidence. It's presence in an otherwise solid case solidifies the case. But it's absence in a kind of "open ended" case doesn't necessarially absolutely prove innocense.
Obviously the defense attorney is going to hammer on the absence of GSR because, well, any port in a storm, but it's only going to really effect the court of public opinion. If this goes to trial a state expert is going to explain essentially what I just explained (though he'll explain it a whole lot better).
I agree with you that a lot else about this case is "fishy" and I certainly am not trying to make a case here that the parents are completely innocent or that the alleged shooter is definitely guilty. I just wanted to jump on the GSR thing as a kind of PSA.