I dont' think this is at all true. You'd have to know a) whether that YouTube rumor is true b) what the content of those proposed scenes actually were, and c) whether a director who decided to try and save his own film instead of melting down could have come up with storytelling alternatives to get his characters to the same place in the arc that they'd have been with those scenes intact.
it's not the greatest example, but Rothman cut Bryan Singer's budget by half on the first X-Men, with not much notice, and a really short shooting schedule ahead of him. Fucking dick move, right? Singer, whose biggest film to that point was a well-regarded independent film, could have thrown his hands up, spiraled out and blew up the set so bad the producers had to call in a bunch of friends to try and salvage the film while he pouted on the sidelines. Instead he turned in a definitely compromised, but still workable film that ended up being a genuine success that went on to help kickstart the superhero film renaissance.
