That's why HR departments need to implement a "talk it out" program. Set aside a private conference room, just a room with a small table and 2 chairs, where people can talk out their issues, with documentation of the issue that was discussed, and signatures from both parties indicating that the discussion did, in fact, take place. The forms are deposited into a locked box (via a slot, obviously) in that very same room, to be collected weekly by HR, but no action to be taken aside from filing the form away in the complainant's employee file. It should then become HR policy, when someone comes in to complain about a coworker and does not have an appropriate "talk it out" form in their file already, ti simply hand them the form and tell them to talk it out. Attach a 3 strikes rule to that (e.g. if you come to us without the form 3 times, you are the problem) and make the forms openly available without needing to contact HR, and you have a way to weed out people who just like to complain.
Of course, if the form is on file, the complaint needs to be heard. If the complaint refers to the incident discussed on the "talk it out" form, the complainant should be reprimanded; if the complaint refers to a continuation of the behavior discussed on the form, the person the complainant is complaining about should be reprimanded.
Make attempting to work things out like normal adults an actual corporate policy and attach real consequences to not doing so, filing false complaints, or otherwise the system, and watch the problem solve itself.