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It was likely just a lag type glitch on your end.
Sometimes i see people 'riding' their horses while standing on the saddle running. lol
I suppose that could be, but when I've seen it occur they usually remain mounted for the duration of time they are in the bank, at least 15 minutes in one case I remember. Also I remember another person in the bank commenting about it.
As far as people running on top of the saddle, lol, I've heard that this is a bug the developers decided not to fix since everybody universally finds it to be so hilarious.