Shouldn't we assume that anything online is paid advertising? I mean, someone is paying for it. Same thing for newspaper and medias in general.
It would be sad if we have to go down that road. There's a guy who maintain a website about old local railroad in my area (and you are NOT allowed to share his content on Facebook), no one is paying him anything. Should he then be forced to label his content as: "Not sponsored", if he don't want readers to assume that he's sponsored by someone?
I'd say you where closer if you had suggested just labeling Instagram as an ad platform. Anyone with more than X number of follows, assume that their posts are sponsored.