The Crawford connection
Much has been made of the fact that the screenwriters of this film were ticked off at Crawford and supposedly based the lead character on Crawford. But honestly, I don't see many parallels between Margaret Elliot's story and Crawford's own.
The only obvious visual cue takes place during the screen test, when Davis' hair and makeup are definitely reminiscent of Crawford's style. (Interesting, when Bette was trying to sound "young," she spoke in that rather annoying voice that she had previously used in "Mr Skeffington"!)
The one real zinger in the script, that was obviously aimed at Joan, comes right near the end when the screenwriter is describing his idea for a film about a self-involved actress. That little speech was very obviously a jab at Joan from beginning to end---heh.
So, I can see why Joan turned down this part--I don't blame her a bit. I can't imagine her wanting to work on the project when she was on the outs with the writers. Also, I can't see her having any desire to play a washed-up actress when she was so desperately trying to hold on to her own place in the Hollywood hierarchy---she wouldn't want the audience to connect her in any way with a has-been! (And I say this with great fondness for Joan.) In a way it's a pity, though, because I think if Joan could have loosened up a bit, she would have been great in the part.
Unfortunately for Davis, I'm afraid the general plot arc in "The Star" was more in tune with Bette's career at this point in time, rather than Joan's. Joan had a decent run in the fifties, continuing to work regularly as a top-billed lead in films that generally made money---and in some instances were quite good. Bette's 1950's film career was much spottier---she wasn't finding as much work as Joan, and she really only had a couple first-rate films during that decade (and some that were really pretty bad).
It's a shame---Bette proved she was absolutely at the top of her game with "All About Eve" in 1950---she should have been making great films for the next decade, one right after another. But it seemed she just couldn't get the scripts, couldn't find those good parts.