I meant my comment to be "only in the most general sense." I agree that the film terribly mistreats Bernstein's music, just as the 2 other films I cited treated the songs of Rodgers and Porter.
Bernstein's Broadway music didn't get proper treatment in movies until West Side Story arrived. However, his score for On the Waterfront was certainly given the respect and adulation it deserved. It has even been well preserved in its entirety on CD (with Bernstein on piano in one cue).