When Sony Pictures Entertainment decided to make a movie focusing on the death and dementia professional football players have endured from repeated hits to the head — and the N.F.L.’s efforts toward a cover-up — the studio signed Will Smith to star as one of the first scientists to disclose the problem. It named the film bluntly, “Concussion.”
But in the end even this studio, which unlike most others in Hollywood has no significant business ties to the N.F.L., found itself softening some of the blows it might have inflicted on the multibillion sports enterprise that controls the nation’s most-watched game.