I spent four or five hours in a scene with a t3 that was mostly 1-on-1. It was in public, but nobody else lingered beyond walking through. Have engaged in other shorter scenes and interactions with them before and since. Still at Invitation 0.
Also done a lot of 1-on-1 RP with monsters, which are mechanically t5. Not sure if they’re exempt, but have not been punished for it.
I can’t speak to daily private interactions and how fast those might increase it, but I don’t think there’s justification for avoiding t3s entirely based on Invitation alone. Casual interaction does not seem to be a problem, at least. Again, can’t speak to being besties.
Just don’t want people thinking that hitting 10 is inevitable from interacting with t3s at all. You can definitely RP with them!