The incident you’re thinking of is probably when Maverick’s wingman freaks out (sorry I can’t think of how to put this more artfully at the moment) by the encounter with the MiGs and has to be talked down by Maverick.
Which may explain its close resemblance to a T-38.
Great movie line, in “Jet Pilot”: When Janet Leigh, as the defecting Russian fighter pilot, brings her T-33 with a red star painted on it into the American base, John Wayne gets to say “So that’s the new MiG, huh? Sure looks like one of ours.”