Was he really furious that he lost? I didn't see Bobby Darin's performance in Captain Newman, M.D. , but I did see the movie Hud and Melvyn Douglas only had one great scene in the whole movie. That was it. I didn't know you could win an Oscar for one scene. I'll have to check Darin's performance out.
In the movie, when Sandra Dee says something about Melvyn Douglas dying, I think Bobby Darin says, "He's dying? I'm the one dying! Way before he was dying, I was dying." I'm curious now if this was true.
All I know about Darin is from the one book I read about him years ago, one that was written by the son he had with Dee.
Two seconds of googling has told me that Darin died in 1973 and Melvyn Douglas died in 1981, the "dying" old actor outlived the young one by 8 years. And Darin did believe he was dying, he had a congenital heart condition that couldn't be cured in his day. He spent his whole adult life knowing that he wasn't going to live a long life, so if he really said "I'm the one dying" then he was being honest.