Ok, so this is an interesting issue, I'm still trying to get to the bottom of it but here's what I've found out so far:

I'm under the assumption that canceling the damage event for damaging a sitting parrot should also prevent the parrot from standing. However, the parrot stands up (no damage taken), provided that the owner of the parrot is online.

If the owner is not online - it will stand up the moment the owner joins.

I've been using GP 16.7.1 with a parrot sitting inside an owner's claim, and will shortly be making a small plugin that simply cancels damage events for parrots to further test this.