That's not my misconception since I know that a bunch of territory starts decaying if it's detached from the territory root (it's a useful strategy when invading).
Saying "really it's about being connected to a territory root" is what I mean, that is, that's how it should be.
I was wondering if buildings not connected to territory root would still decay if their "footprints (their size) always be the territory of the building owner", because said like that sounds like they would be "self-sustaining" territories, but maybe the workings of the algorithm are not so straightforward (I'm just thinking of it as: you move the borders, and if a building falls into enemy territory, it decays, but with what you propose that would seem an impossibility).