I have the opposite problem, My horse is possessive of me! She hates when I pet other horses, if she's standing by she reaches her neck out at the other horse and her upper lip flares. She's not too keen on me talking on the phone, especially when I take a call while I groom her. If I stop to talk to another person with her, she acts as if she wants to be in on the conversation. I feel like she's saying "mommy, mommy, look at me, me, me!" She seems to be so used to having all my attention that she doesn;t know what to do with herself when I'm diverted. Lol.
I guess I don't truly know if I have a one person horse. I do know that I am the only person that has truly owned her and I pretty much exclusively have worked with her. She started the handling process late, at 4 years old. Before then she was desensitized to people, yes, they would feed her carrots and throw her food, occasionally pet her, but it was just her and her sister wandering in a huge field. She had no prior vet, farrier, or dental care, AT FOUR! She's pretty acclimated to anyone handling her now, I mean she's young, so she has her moments, but ask joe schmoe to take it to the ring and she will test you out. I guess if anyone is up to that test and passes she'd be a multiple person horse, which case in point, has happened with all the trainers I have worked with. They worked through her hiccup and everything was fine after that.
Maybe this has a tendency to happen to horses that have only ever had one owner, or horses that have been abused and then finally find relief in one owner? I don't know, perhaps I am romanticizing things.