This isn't true. Mike Ditka of the Chicago Bears did it in 1985. And Kubiak wasn't even the second person to do it, but the third, since Tom Flores did it first in 1981.
It surprises me a little that Nance got it wrong and likely just accepted what a researcher told him -- Flores was well known, though not a huge personality, but Mike Ditka was and still is a major public figure, bother as a coach and Hall of Fame player. Only last week, ESPN had a 2-hour special on the 30th anniversary of the Chicago Bears winning the Super Bowl, and Mike Ditka's involvement with the team -- both as the coach and a former player -- was a significant part of the documentary, with Ditka himself getting a lot of airtime as an on-camera commentator. But people can fall through the cracks and makes gaffes, it happens.
What most surprises me, though, is that throughout the broadcast, no one called in to the announcers' booth and corrected any of Nance's three mistakes.