I'm not BSK but I do have an opinion, albeit a long one
Deer are deer regardless of property lines. Their nature is static. And on public ground a buck doesn't get old and big by being a stranger. He got old because he knows the area, knows where to be and when. The only way to acquire that kind of familiarity is by spending a lifetime in that area. That means yes, you can run a camera program on public land and get the same kind of data as you would on private.
That said, I've never heard of anyone attempting it because fear of theft. Could you imagine hanging a dozen cams on a public tract and leaving them in place for several consecutive years? Pretty risky. However if you did I 100% believe you'd see the exact type of cumulative data you'd get from private ground.
The one exception is that you'd likely have to shift camera locations as the resources and movement patterns change. Public land isn't managed to have static spots like food plots, mock scrapes, water holes, managed bedding areas, etc that dictate movement. On public that stuff is in constant flux so the deer are always adjusting. But the deer aren't leaving. It's the same deer.
I've heard of guys having multiple year hunts for a specific buck on public and have done so myself. That's only possible because the buck lives there, at least periodically.
Think of the clear lottery tank with all the numbered balls. That is a buck's home range and each ball is an individual buck's core. Notice how that core floats all around but is contained within the tank. In my experience that's exactly how it works in the deer woods, regardless if you're on public or private. A buck's core floats around according to his specific needs at the time, whether it be food, does, or safety. They don't recognize property lines or ownership. That's why we see a buck on camera every day for awhile then poof he's gone. Just when we think he must be dead poof he shows back up. It's nothing more than his core bubble floating across our property. And it floats across lots of properties both private and public.