Not only no, but hell no.
Carson totally lost the 1971 team during the 9PM practices for the 1970 Sun Bowl during Finals Week. By the start of the 1971 season we had high hopes, but Carson and Tom Moore (yes, Peyton Manning's Svengali) had totally screwed the offense to a fare thee well. I never saw Brent Cunningham and Herman Lam winded until Carson & Moore started using them to shuttle in plays. And they used Cunningham as a decoy at WR!
Once Carson went into "bunker mode" after the Army loss, he decided & voiced to us WTTE "If I'm gonna get hung for the offense, I'm gonna call the plays." As a defensive genius who knew how to deconstruct an offense, he thought he also knew how to also build an offense. He did not.
McAshan's dismissal had nothing to do with QB-Coach relationships. Who was Fulcher's QB coach in 1972? The most likeable, easy-going guy on the planet, Steve Sloan. That was all about Eddie demanding a dozen or so free tickets for the UGag game on Thursday before Saturday's game in Athens. All players got a minimum of two, starters and seniors got four. Out of state (like OH, PA, Chicago, etc) guys always made their tix available to the home grown guys. Fulcher told Eddie no, Eddie skips practice TH & FR, misses the bus & was turned into a footnote.
As for the Rice game, Eddie threw 5 TD passes, but he also threw 5 INTs. We were up big, down big, and lucky Jim Owings & Jimmy Robinson were on our side. IIRC, Rhino also tripped over a yard line marker or he'd had a pick-six in the game.