That's the price you pay for not watching influence.
Hard to tell, there are several factors that come to my mind that can disagree with that statement, for instance, that influence comes from an ally that reached a point in the ideology tree that give him a boost to his influence. Anyway, I won't go any deeper. Just that there are cases when, even if you check influence, you might be in a scenario where you cannot do much about it (especially from this perspective of flipping starbases).
Note that we're not talking flipping influence starbases
I do not understand this, are you saying that you can flip all starbases except influence's one? if that is what you mean that make little sense. I mean, you can influence a planet that have an influence radio that potentially can flip other planets, and since starbases can be influenced as planets do, that means that influence starbases can be flipped too, right?
The idea that you should be able to build military starbases inside other people's influence willy-nilly is just wrong on the face of it.
Starbases are used not only to support your planets, but also to give you a boost in reach (like a gas station) and military control of a sector. That means that, most of the times, you need a starbase outside of your territory (think of it as an embassy, just without permission). Also, in real life, when you want to invade a country most of the time you must have a small piece of land controlled by you where your soldiers can rest, eat and have a better tactical advantage. It is not that people cheat on that, it is that is a tactical maneuver that nobody allows but "everyone" uses.
Now, what I find a little silly too is that in your turn you can build a complex starbase with enough constructors, but face it, it is a game and if we were bounded by reasonable "real" time we would die of boredom.