Oh lord no. USAF F-4Cs,Ds, and Es along with other Navy Js and Bs had already scored many kills, as early as 1966 I think. Col Robin Olds leading ....I think it was the 4th fighter wing F-4Cs, baited N.Viet Mig-21s up acting like F-105s in 66 I think, nailed 7 Mig-21s w/o loss in one fight. He was a P-38/P-51 ace in WW2 with around 20 kills I think. They used Aim-9Ds I believe on all the kills. There were alot of kills made in 72. I say "I think" alot because I may be a little off on dates, but I know that it occured. I remember it as well since I was a kid, but if you google it, you can find all sorts of stuff about it. Olds scored two of the seven kills in that fight, and got another Mig-21 a bit later. An F-4C in his markings (Scatt IV, a P-38 and two 51s having been named that in WW2) is in the USAF museum.
Showtime 100 was the CAG bird flown by Randy Cunningham in an epic day over N.vietnam in the linebacker strikes in 72. He had already nailed two Mig-21s in a fight, and as he was withdrawing he was jumped by a very proficient pilot in a Mig-17, which has been reported as being flown by a N.viet ace named tomb or toon or such, but this has never been established. either way, it was a WW2 style fight which Cunningham won. On Utube I think there is the episode of "dogfights" that details it.
He had already scored two kills in that F-4J, which made him one of two American aces of Vietnam, the other being capt. Steve Ritchie, who scored his 5 kills in F-D and E, in 72.
Check thelink above to a very good book about the air war over Nam. Mucho detail.