When I purchase a star base from a race in its space and I don't have a open borders treaty, it should not affect my relations with that race.   A Star Base cannot be moved, and my purchase of the star base from its original owner is with their approval so it stands to reason that the star base would stay where it is.   As it is now, the race that sold me its star base gets annoyed that it is within their borders.   For one thing, the presence of that star base can be what makes it possible for me to open a trade route with the race in question, which is something which benefits both.

Even if it were a military star base, there is no reason for the race to be upset unless I send armed ships within the border as military star bases do not attack by themselves.   (Perhaps, the sold star base would be "upgraded" to contain no military technology when sold.  Upon purchase if it is within the borders of the race it is being purchased from, then the installation of a hostile technology by the purchaser would cause annoyance:   Hostile tech being:  Conversion (brainwashing) tech and/or military/defense. 

Non-brain washing tech such as entertainment centers, shopping malls should not be considered as hostile.

I could see players exploiting the annoyance for a foreign star base within the border being abused by players specifically purchasing a star base from one race and giving it to another race in order to get that race to attack the new owner of the star base.