Would I hunt a spot with a stand? Yes, if I thought it was a good one. That stand could have been there for years. I will give someone a wide berth if they are in the stand, but stands don't save spots. I duck hunt public lakes from time to time, and always appreciate it when someone decides not to pick up their hulls. Those spots go on the map with my spots too.
Would I hunt someone else's stand? No. It's their property. And I don't trust someone else to hang my stand, especially if I don't know how long the straps have been rotting in a tree. Hang yours on the same tree or the tree right next to it or even facing it so you two can scowl at each other all morning, but don't trust your life to someone else's dryrotted ratchets.
Would I take the stand? No. It's someone else's property, and they may well have permission to leave the stand there.
Unless there was actual damage (decent sized trees being cut/damaged, offroading, etc), I wouldn't waste the manager's time.