I'm certainly no expert, but Top Gun was realsed in (I think) 1986, a year or two after the Firm's debut, so I don't think Top Gun had any effect on the decision to cover the song. Personally, I don't really care for the cover tune because the original is really overplayed. When I listen to the Firm, that's probably the one song I skip over 90% of the time.
Up until about 15 years ago, I played in a classic rock cover band around DC (some of the same places Dave Grohl played with his pre-Nirvana punk band, we grew up in the same neighborhood, but that's a different story).
Anyway, I tried and tried to convince the band to do a Frim cover. They finally agreed to do Satisfation Guaranteed. When we played it for the first time, I was thrilled to hear some chicks in the crowd actually recognize and sing along with it!! This was somewhere like 1992-93 when the Firm was just a bad dream to most folks. So I was glad to see that they were gone but not forgotten, and it's just as thrilling to see the same on this thread so many years later!