As a random player with no authority whatsoever, I
think the short answer is that there are no explicit/separate "rights" for charmed pets. However, if you get your pet killed, that is still you killing a mob in a sense, so I'd think you could still say "I killed it last" for the purposes of claiming it as a camp.
Thus, if you charm Foo, and Foo dies, Foo is still your's as long as ...
- you are at Foo's spawn point, waiting for it to respawn within a "reasonable" amount of time
- you aren't claiming any other camps (which could only be true if you're using Foo to grind non-nameds; if you want to use him to kill a second named called "Bar", it wouldn't be)
If the first point isn't true, all bets are off (as they are with any camp). If the second point isn't true, you can still recharm Foo ... but if anyone else lets you know that they want Foo (or Bar, or anything else you're camping), you have to relinquish your claim to Bar (and anything else) the moment you charm Foo.
But also ... if Foo drops loot people want (eg. you charm the Skeletal Hierophant in Sebilis Crypt, who drops the popular Heiro Cloak, and wander around Sebilis killing non-nameds with him), the GMs might consider that "disruption", as you're denying others pixels ... so as with many ruling questions there isn't one clear cut answer, and it would depend on the GM call based on the circumstances.