I wouldn't worry too much about what the AI civs say about your influence starbases. There's a big difference between using them to bring your own planet out of revolt and deliberately positioning them around an enemy planet with all the influence modules going.
It would be very stupid of them to start a war over one influence starbase that's showing just enough reruns of Neighbours to keep your citizens happy. Because now that war's been declared, you conquer the planets that are exerting all that influence over your planet, and the next system just to teach them a lesson, and before you know it stars are exploding, planetary debris is wooshing all across the galaxy, and to think that all you wanted in the beginning was to keep your citizens from switching sides... well they can't switch sides now because the other sides have been vaporised.
But then the AI can be a bit dense sometimes. They honour alliances without taking a look at what firepower the enemy is packing, what sort of plan they have, what kind of backup they might have, what they have to lose if attacked. They try to hunt down scout ships and end up being ambushed by a superior force (in fact, I keep ships hanging around waiting for them to do just that). They'll stop their transport and send it back to friendly territory if the target planet pops up a defender, no matter how weak and how easy it would be station a fleet nearby to mop it up immediately. When deciding to pick on the human player they never do the smart thing - let one of the other empires try first.