I helped with the Elk Monitoring program here in Wisconsin for the DNR. Basically.....trail cams on public land. Many of these were close to access roads, some were fairly easy to see when walking by. I never had one taken or molested, nor did the program in general have a problem with either theft or molestation. BUT, the trail cams were in a protective lock box and secured with a heavy duty cable type lock. I had several pictures of folks coming up to and fiddling with the cameras, giving the finger and shooting the moon(cameras were obviously marked as belonging to the DNR, and some had wolf collar receivers attached), but never found one gone or damaged. Take similar precautions and I think one would have similar results. I would first contact the local DNR/F&G to see what the regs are for leaving a trail cam on public land. Here, property intentionally left on public land tends to become public. Leave a tree stand/blind on public land unattended for over 24 hours and it becomes the property of anyone who wants it. Rules like this are so folks don't "stake out" territory in attempt to keep others away. This is why the DNR requires any portable stand left unattended for even a few hours to have the owners name and address attached. Since I don't use trail cams, I don't know what the state's stand on them is on public land. If I were to use 'em, I'd want to know if it was legal to hang them. That said, around here, it seems there is a very high chance of trail cam theft/molestation, even when paced on private land with limited access. My oldest son has a hunting parcel situated right in the middle of several other large tracts whose primary purpose in for hunting by land owners.
All of these are limited access. All have a high incidence of trail cam theft, so much to the point, my son no longer uses trail cams in his woods. He does tho have several monitoring the buildings.