If there were only those two people involved that's possible. But in a situation with onlookers the bull-headed 'winner' will gain a reputation for being aggressive and unlikeable, while the the 'loser' will seem reasonable and professional. If our 'winner' persists with this behaviour they'll end up ostracised at best and more likely ousted from their position because no matter how correct they are, that sort of behaviour is always a net negative overall.