I think the OP makes an interesting point. Due to my volunteer engagement, I have been in a lot of photos at a lot of events with a lot of people. Some folks I see routinely at meetings or civic events, some I am "friends" with on Facebook, and a couple I've had business dinners or lunches with. Very, very few of these photo companions have ever been to my house or ever will be. Even our dinners or lunches involved recruiting support for ideas, candidates, projects, fundraising etc.
I "know" the people I'm pictured with to the extent of knowing their names, job titles, and potential usefulness in advancing my causes-it's networking. I don't know their addresses, their spouses or offspring, or their proclivities.
Over the years, I've been to a lot of functions with people that I do not remember. I'm sure I've even spoken to a lot of them. I am terrible with names/faces, which is weird because I am outgoing (or at least pretend to be..I'd rather be home!). I have a lot more people remember me than I remember them...not sure if I'm just weird and easily remember for that or what!
But I have to say I would not forget meeting a prince. Having said that, I do not regularly interact with famous people like Trump has over the years. Perhaps a prince would stick out more to me because it would be very unusual for me. Or maybe Trump is just trying to distance himself. Who knows.