You're not required to give up the spot.
If you believe that they were genuinely wiped and made their way back with delay, then you may want to do so.
If you just don't want the hassle, then you also may want to give it up.
But the policy on this is that so long as someone else isn't engaging a mob, that mob is free game. So technically, you and they could hunt in the same camp without breaking the rules. It's just not very feasible.
If you tell them you have this 'spot' and aren't giving it up and they start trying to steal your kills after you've engaged a mob, that's when it's time to tell them you're turning in the logs from the event. Most people will reconsider at that point. Ones who know the rules will back off if they know they're wrong. Ones who don't will either back off because they might be wrong or often get really obnoxious, which makes it a clencher with the log.
Personally, I try to deal with people as nicely as possible. I'll walk off before I get into a confrontation over some mobs. The people may or may not go on my 'do not **** on them if they are on fire' list, depending on their behavior, but I'll just go kill something else. It's just not worth it.
I was in a group in MM the other day and the group decided to muscle in on another group. I left. Plain and simple, I don't want to be involved in that sort of behavior.