IMO they weren't camping there. It wasn't a legal spot (they might actually have had an argument about whether they would risk it). I am speculating that it happened in late afternoon or dusk, soon after they got there.
IMO she ran trying to get away from him, and he caught up to her. He killed her on the spot. She might have tried to hide from him in that cluster of vegetation. This seems to me more likely than him dragging her there.
I think they were camping there (and that Brian did leave the van there for a couple of days while he walked and hitchhiked). You're right that it wasn't legal this summer, but in general in NF's in Wyoming, it
is legal and very little would have happened to them, other than to be asked to move on. It doesn't look like the van was ticketed, so I believe the campground host (probably no ranger) was busy enough without having to try and get people not to camp there.
Brian and Gabby may have only known the general rules for dispersed camping. Here's the Department of Agriculture's webpage about dispersed camping:
Bridger-Teton National Forest - Dispersed Camping Areas (Undeveloped Campground)
Lots and lots of people will just read that first paragraph and think they can camp anywhere. They don't keep reading to learn that a handful of dispersed campgrounds don't allow it. Spread Creek is one of those campgrounds.
We camp in similar situations a few times a year, and IME, there's either no one around to check or that person allows the errant campers to stay one night. In my experience, this person is always a seasonal employee who has a satellite phone and many duties to fulfill, such as putting more toilet paper in the porta potties and cleaning up trash from campsites where numbskulls have left it. We even have dispersed campgrounds that we love and prefer due to the personality of the host, who has been doing it for more than 20 years.
One of the big problems in this kind of camping is that people without a site will beg others to stay on their sites and sometimes come into your campsite late at night to do this begging (and once, some people just started putting their tent on our site - we had to get the host to come over; he relocated them to a suitable place that was unnumbered for one night, as it was late and the road out of the mountains had drop-offs and was very twisty). He told me that there were a handful of these "overflow" places that were unnumbered, basically pull-outs on the road - they were there for just this purpose.
I too believe that Gabby tried to run from Brian, resulting in her being found where she was. You're right that Gabby may have known it was an illegal spot and they could have argued about that too. If she did run, she ran away from help and not toward it - but he may have been preventing that. Or, like many abuse victims, that was her first impulse (again, to protect Brian, to avoid the embarrassment). She may even have been screaming - the main campground is far enough away that it would scarcely be heard or noticed. People scream when they see a snake or even a spider, so screams are normal in campgrounds anyway (a couple of screams, not constant screaming).