Air carrier pilot reported taxiing to the gate on uncontrolled BNA ramp and passing behind an aircraft under tow. Reporter was later informed that they may have taxied too close to the other aircraft.

Narrative

On Day 0; we arrived in BNA. After a complex inflight troubleshoot during a Slat/Flap Jam procedure; we landed uneventfully and taxied to Gate X. We entered the uncontrolled ramp and proceeded to Gate X to park. There was an Aircraft Y under tow that was repositioning. We proceeded to pull into the gate as the First Officer and I felt there was adequate clearance and the other aircraft was stopped. We did not taxi between the aircraft and the gate; but only behind the stopped Aircraft Y. After parking; and while talking to Maintenance; an airport representative came to cockpit and stated the tug crew felt we got too close to them. Our FOM states on page X that when conducting ramp operations that we should not taxi between a gate and a aircraft under pushback. We did not. We were behind the aircraft in question. It also states it is the Captain's responsibility to assure clearance which in the opinion of myself and crew we did without any threat.As the ramp is uncontrolled; we made the decision to continue; but in hindsight; if the other crew felt we should have waited for them to continue until well clear; we could have done so. We did not hear any complaints from them on the ramp UNICOM that they should have been monitoring and communicating via.Since we thought there was no issue and that the case was closed; I did not initiate a report; but per the suggestion of our Company; I am submitting this report to explain the event of that evening.