I attempted to use the ctrl + x method of destroying the object. It did not work.
There are several things however:
The only place I found that mentioned the command was not in the control window in the game but the actual manual itself. It took a very brief description that said to the effect of "on capturable target object" a very vague term...In addition, the civ spire is minor faction object, not an AI object. Could the "capturable" tag somehow get messed up because of this?
So I guess this is a dev question: What must be done to destroy the station?
It cannot be scrapped, so you can't destroy it that way. You can't target it using ctrl + v. The tooltip clearly, explictly says they can be destroyed. I assumed you would only destroy it and not capture it because you could not recoup the AI cost of destroying the planet by defending it so simply wanted to cut the increasing AIP.