Anne Boleyn wants to be the very best, like no one ever was. But if a woman becomes queen and no one is around to see it, is she even queen at all? Not in her mind.
Basically, Anne doesn't do anything if she can't brag about it. In the lead-up to her being crowned as the queen, she organizes ostentatious parades and a coronation party to end all coronation parties. She'd have hired the Magic Mike dancers if they were around back then.
Eventually, she makes a big a demand from Henry: "They are England's jewels, given to the queen. If I am to be queen then I must have them. If she is queen then she can keep them. Choose!" (35.116).
Yes, Anne wants to be confirmed as queen, but more than that, she wants to take these jewels from Katherine. Anne may be queen, but she's not above going, "I'm queen and you're not, nyah nyah nyah."
It's not hard to understand why, though: the only thing making Anne the legit queen is that Henry has legally divorced his wife and married her. But, um, technically, in order to do that, Henry had to break with the freakin' Catholic Church and make his own church. Not everybody—surprise, surprise—was okay with that. So in a lot of people's minds, Anne was not legit—no way, no how.
But hey, if she can get those crown jewels, it sure can't hurt.