Wasn't public land, but participated in this very "discussion" last year with some hunters. Couple of guys on the adjacent property shot and wounded a six-point buck. I could hear the buck coming, and he was moving well. Came across the property I was hunting, went right through the middle of a sizeable pond, and was dropped by another guy with a well-placed heart shot.
I was talking with the solo hunter when the first two showed up. We examined the carcass together. There was a wound through one of the rear legs, and the heart shot. Pretty evident that the fatal shot was the latter. The original two didn't argue the point, congratulated the solo hunter, and headed back off the property.
Rule I learned was that the killing shot takes the animal. However, I'd personally not argue the point except maybe in a case like this, where there were two obvious wounds, one of which may likely not have proven fatal.
Don't know what the solo hunter would have done had the first two guys tried to argue that the deer was theirs. With me standing there, he wouldn't have felt outnumbered, and we were on property that he had permission to hunt and the first two didn't ... Nevertheless, in this instance, the "killing shot" was pretty obvious.
As far as continuing a hunt in an area where a deer has already been taken, keep at it. I took a nice 8-point this year, first thing in the morning. Had it dressed and dragged out and was back on the same stand by 9:30 a.m. Just after 10:00, a second buck walked through on almost the same track as the first. Didn't seem stressed at all. And if there are a lot of deer in the area, and a lot of hunting pressure (read that a lot of hunters moving around), quite likely that they'll push something through for you.