Didn't NFL films offer it to the Steelers but they turned it down?
The way I heard it, Dallas' owner Tex Schram annointed the Cowboys "America's Team" before one of the Super Bowls. NFL Films brass went to Art Rooney Sr. and asked him what he thought about Dallas' new nickname, Rooney replied 'We don't want to be America's team, we're Pittsburgh's team.'
That said, It's inexplicable why there aren't more Cowboys in the HoF. Like it or not, Bob Hayes has been black balled because of his drug problems in the 70s. Perhaps Cliff Harris and Charlie Waters weren't as good as Cowboy fans remember. Hayes, Rayfield Wright, Drew Pearson, Lee Roy Jordan are absolute HoFers, and deserve to be there as does Troy Aikman. Michael Irvin...?