SFO Tower Controller reported a NMAC with two arrivals after one aircraft took action to comply with a TCAS RA.

Narrative

Aircraft X; on final for Runway 28L; transmitted a question about Aircraft Y; turning to final for Runway 28R; their flight path; and intentions. Aircraft X then came back and said they were responding to a TCAS RA and going around. We (myself and Local Control (LC)) notified the Controller in Charge (CIC) of the TCAS RA; noting that we agreed Aircraft X concern; that we both observed that Aircraft Y appeared to cross through centerline; it was likely significant and possibly a NMAC; and that we were going to Brasher Aircraft Y. After landing; Aircraft Y was given the Brasher and Ground Control (GC) provided them with the Tower phone number. Upon review by the staff specialist there was no issue or loss and when the pilot called the Tower; they stated that they did not cross centerline; and the CIC said that they did nothing wrong. Upon my review; maximum separation at one point was .12 laterally and 200 ft. vertically; with the aircraft at one point being within 100 ft. vertically. Furthermore; the replay with centerlines depicted; clearly shows Aircraft Y flying through centerline and despite the radar replay not having centerlines; and also depicts it. Had Aircraft X not responded so quickly; the two aircraft would have been significantly closer; especially considering the already close proximity of the finals. In the essence of safety; this issue should not have been brushed off so easily by the staff specialist; nor the CIC. And despite; the CIC's unnecessary comments; saying something and giving the Aircraft Y pilots the Brasher is not to 'take away some pilot's license'; but instead to highlight a potentially significant issue and error on the part of a pilot's actions. Safety is always the first priority and making it seem as though the mistake is insignificant leads us down a slippery slope.