I just realized I’m a derp and had a hunter on a different server from when I first started that does not have first aid. The perfect opportunity to test this myself and I spaced it 
So at first my thoughts were “Wow maybe there’s something to this, it still rubberbands sometimes but it fixes itself and my pet seems to never get itself fully stuck.” Further testing however revealed that it may just be map dependant, when I changed maps from tenet garden to tenet church b1 i was eventually able to break my poor companion’s ai and leave it in the dust.
So in the end my thoughts are that if first aid affects these particular bugs at all it has to be in overcomplicating the pet’s ai. The theory runs that the scripting of the ai is fine but in practice it does not process well or have any way of dumping it’s queue and clearing itself up for the next input. In adding other if/then/else statements with passives (bear with me if I sound retarded I took a c++ class years ago and that’s it) it merely aggravates the problem that already exists by necessitating that it process yet another variable.
My barely educated ramblings aside, I think it may just make it slightly easier to bug out rather than causing anything by itself. So far this seems completely avoidable by simply not spamming commands and waiting for coursing to “run it’s course” (bah dum tiss) before issuing more commands. 