After like a few HOURS traveling, two people finally arrived to our village for a visit.
They entered under the shroud of visitors, and all was well until they've reached the part of the village that is claimed by my p-claim. My p-claim gives Light Blue people Trespassing rights - and they were marked as Light Blue. However, they couldn't enter my claim or interact with stuff inside it (like doors into houses).
To make it even 'better', one of them crashed and was not able to come back because she was inside someone else's claim, so after hours of walking she was ported back to her HF.
I'm not sure why/how things worked out this way, or if it is intended or not, but I'd like to say what I think nonetheless:
p-claim rights should override the visitor buff. It's like living in a condo and bringing some friends. The "public" area of a condo has rules and I have to tell my friends to respect these rules, but the moment they walk into my apartment - if I tell them they can use my fridge, take some beer home, break my old TV, etc... that's not the condo's concern

Also, I'm aware that if we were grouped when they got in, they'd have all the rights - but other villagers don't know them and wanted them to have the visitor buff. That's exactly what I mean with the condo rules: the game should allow you to bring people to do what they will inside your p-claim in a village even if the village itself will have them as visitors only

I understand that due to game mechanics, it might be difficult to work that out... Or I'm not sure what went wrong (?) Maybe it went wrong because my p-claim has no gate inside it so the buff could not "refresh" or something? (?) I don't know...
Anyway, just letting it out...