I would not suggest to claim anything without having knowledge about it's origin and possible owner(s), no matter if NPCs or PCs.
The first situation that comes to my mind is a simple player-character-knowledge-conflict :
Give the situation, that player A does not know about the origin of place/item A, and claims it to be his, and consider:
Player B HAS that knowledge, and his character char B as well, char B might "correct" the statement of char A, or inform the owners about char A's claim, or spread the word about char A being a character without honour.
--> all resulting in ingame-consequences the player of char A did not expect and as well possibly not want, except if he does not mind his character having the reputation of a bandit or thief.
A second situation could simply implement ruining some GM's plot by having a group of players spreading wrong facts based upon such claims, thus feeding wrong info to other players who then lack an important link in the information chain needed to solve some plot.
All in all, it might end up wiser and less troublesome to "own" things "officially".
