It seems I'm doing a lot of testing while occupying a city tonight!  I just noticed that cities of other empires that I occupy count as "mine" when determining the influence cost in creating a new outpost.  In the screenshot below, I can found an outpost adjacent to Rome (mine) and Athens (theirs) for 70 influence, a value that goes up further from either of our cities, and is large (90+) far from mine and adjacent to theirs.

Maybe this is intended?  It feels a bit weird, but I guess an occupied city could be considered a place to build out of?