My guess is it's somewhere in between what the movie has and what the press says was that they didn't get along. Since everyone has always said Mantle was a great teammate, I'd say they probably got along but maybe not best buddies like the movie portrays. Artistic license perhaps.
As for the Phil Rizzuto character, Joe Grifasi was pathetic. He made The Scooter out to be a total imbicle. That actor gave you nothing that resembled The Scooter.
In the movie, when Maris his his 61st, they should've cut to the real footage of the homerun call by Rizzuto instead of that lame scene with Grifasi. It was so bad, it made the hair stand.