I don't know why you say "Stupidity". This stuff happens.
For instance, the Led Zeppelin classic "Dazed and Confused"...do you know how they "wrote" it?
They were out at a bar, and an unknown acoustic guitarist was playing his song "I'm confused".
Jimmy Page thought it was a wicked riff, and liked the misogynistic lyrics.
So, he completely stole the riff note-for-note, and most of the lyrics, though they changed the title to "Dazed and Confused".
Artists get ripped off.
The only fishy thing is that we'd hear the accusation so long after the release of American Idiot....however it did say that he kept trying and trying to contact the record company. *shrug*
Also, Billy Joe said with his own mouth that he's a dumb person, so if the song elevated them above their previous success, you could wonder if the moron was actually capable of writing it.