I seem to recall Garrett being vague when offering his apology immediately after the incident. He wasn't accusing Rudolph or anyone else of anything, per se, but it really seemed odd that he would lose his cool like that especially after its clear that there is jawing just before he starts swinging. So, it doesn't seem unlikely that Garrett at least sincerely thought Rudolph used the epithet before he started swinging.
Regardless of whether or not it was acceptable, an indefinite ban is not in line. It amounts to Goodell being like a parent that tell his kids that he'll "reconsider" an indefinite grounding as soon as he thinks the've learned their lesson. There are a lot of problems with this approach, and it does nothing to address the larger issue of aggression American football.