Years back a coworker and I were having a small interpersonal disagreement. My supervisor declined to get involved, basically told us to sort it out without wasting work time.
It wasn’t anything serious enough to involve HR (in my eyes anyway), but I spent a solid while annoyed with this response. It took me a solid five years to realize he had made the right overall decision.
He had not played favorites, did not burn any bridges, and caused at worst a mild annoyance to both of us rather than potentially leading one of us to quit.