No, the OP has no obligation to interact with the horse. But here she is.
We’ve had horses in like the OP describes for training. They are young horses that have learned 100% to get their way with their owners (who are usually beginners), and don’t have any idea of personal space. This owner reinforces that she’s at the bottom of her herd of two and he can do whatever he wants. And he does. A flag goes a hell of a long way for most horses and it sounds like this one, too. I’ve never had a problem horse come at me when I’ve had a flag. They almost always back down because they’ve never been challenged a day in their lives and they don’t have the to skills to be alpha when challenged. Esp young horses.They are spoiled brats.
No, they aren’t my horses but I’m sure as hell going to keep them out of my space if I need to. Of course it is not the OPs job to interact with the horse but it sounds like the BO and owner are ignoring the situation. So the OP will have to carry a flag in the mean time or leave.
A horse that challenges someone with a flag is dangerous and mentally not-right and should be isolated, put into hard-core training, or put down. IME with lots of problem horses, it’s not a 50:50 chance that they will back down with a flag. It’s a 99:1 chance that they’ll back down if the person is firm and means it.
We get alot of these horses at the barn because the trainer specializes in starting horses and problem horses. 98% of the time it’s the owner. Or the handler at the time. I’ve never had a problem dealing with any of these problem horses using horsemanship. I did have a problem with a rescue horse who was in with my horse who literally bowled me over when I removed my horse from the pasture through the run-in. I immediately returned my horse and caught that horse, and used a flag to say Oh, no. OH NO. You don’t EVER get to do that. He steered clear of the shed door when I removed my horse but the BO was cognizant enough to immediately remove that horse from that pasture. He went back to the rescue. I know he bowled me over because of fear that his buddy was leaving the pasture and he didn’t know how to heal with that. He wasn’t being bad. I think I delivered the first real training session he ever had - I wasn’t unkind or mean, I was predictable. “You can do that but not this”. He had donated training at the rescue and found a home.
BTW, when my BO took the alpha mare out of their small herd for whatever reason, their gelding mounted the other mare. He’s definitely a gelding and was vying for a new spot in the herd. He was bottom of the herd but was working his way up without the dominant mare.
I’m just relaying my experience and advice. The OP should either a) get that horse out of her pasture b) move or c) always carry a flag and teach that horse that it can roll over the owner but not you. If the owner is OK with being pinned against the ground and hay bales and the BO is fine with that, the OP has to either move or teach the horse to stay away from her. There’s no other choice.