Influence starbases represent an interesting contradiction at the current time: The are an important tool toward the a non-military victory, but they almost always result in war.
The idea of the influence victory is that it is for the players that want to play peaceful diplomatic games and win the the sheer awesomeness of their empire. However, there is a big difference in how the AI responds weather you try to spread influence from planets or from starbases. If you just let your planets be awesome and influential and take over the universe, the AI usually just kind of allows it to happen. Their people start watching your holovids and buying your sweet fashionable cloths until they just decide to be part of your empire. However, if you try to accelerate the process a bit by using influence starbases, the AI is pretty quick to declare war. This means it is basically impossible to use influence starbases offensively since it forces you into military conflict, which is what influence is supposed to avoid.
Now I know nobody wants the AI to just sit back and let you win, but there has to be better ways for the AI to defend itself. It could use its own starbases, or stack influence on the planet you are trying to flip. (btw if espionage is still coming in expansion 1, the ability to flip starbases with spies would really help this game imo). I am a little torn, because I'm glad the AI isn't just letting you win, but to me it really feels crappy to be forced into war for pursuing the strategy that is specifically supposed to avoid it.