I have some insight into possible reasons. The area where I grew up was fairly heavily populated (relatively speaking :)) prior to the Great Depression and continuing on up to about WW II or a bit later. People homesteaded, set up mining claims, and so on. Eventually they left leaving structures on public land. USFS and BLM had a lot of trouble with squatters, hippie communes, etc popping up using those old structures, leaving litter, growing dope, and generally being a public nuisance. One winter we had a ... lets call it a series of anomalous lighting strikes ... and by the next spring, all of those abandoned structures mysteriously burned to the ground yet none which were still legally maintained were damaged. "Hmmm."
I suspect it to be much the same for the structure that the hunters were using ... it simply was not legal to construct anything even semi-permanent on National Forest or Wilderness lands so once it came to USFS attention, they were required by agency policy to destroy it.
Nothing nefarious was required. Didn't have anything to do with bigfoot, it was strictly removal of an illegal structure.
The only structure I know of now which is not on a patented, maintained mining claim or on public land under a long term lease to a private individual is, though unmarked and unsigned, on the National Registry of Historic Places. The rest have been removed ... burned or otherwise destroyed ... by government workers.
MIB