I hadn't noticed the starbase part of this, but I was under the impression that in v1.31 the "we know what you're doing" trigger for war had been improved to avoid false positives. If so, then I respectfully submit that it needs a bit more tweaking.
I’m in the middle of a war with the Iconians and I have a stack of fleets consisting of 4 fleets of 19 fighters each and 3 fleets of 11 transports each. These are located pretty much dead center of a small pocket of my own influence area that contains mostly my planets and a few Iconian planets. On one side of this pocket is Terran space with whom my relations are neutral. On the other side is Korx space with whom my relations are friendly.
I had just saved the game at that point. When I reloaded the game, my influence area had noticeably shrunk, but even so my ships were well within my own influence area (10 parsec’s from any border). I have no other transports on the map and the only other attack ships I had anywhere were at least two sectors away from the edge of my main area of influence. Once I hit the turn button both the Terran and Korx immediately declared war on me because they “know what I’m doing". Around the same time they declared war there’s an apparent ZOC (Zones of Control) recalculation and my influence area expands. Yet the AI can sit with it’s transports right next to a planet of mine well inside my influence area for years at a time and the only thing I can do about it is to destroy the ships and cause a war (yes I know I can buy the transports from the AI but it’s still not fair).