A surprising number of people don't know that it's essentially Twilight fanfic with the names changed to protect the author from being sued.

Yeah, that's an interesting case.

I guess there was no incentive for Stephenie Meyers and E. L. James (and their movie adaptation money banks, Lionsgate and Universal) to sue. But apparently it was brought up in some kind of lawsuit over an actual pornographic adaptation:

In June 2012, the film company Smash Pictures announced its intent to film a pornographic version of the Fifty Shades book trilogy..

Smash Pictures responded to the lawsuit by issuing a counterclaim and requesting a continuance, stating that "much or all" of the Fifty Shades material was part of the public domain because it was originally published in various venues as a fan fiction based on the Twilight series. A lawyer for Smash Pictures further commented that the federal copyright registrations for the books were "invalid and unenforceable" and that the film "did not violate copyright or trademark laws".[206] The lawsuit was eventually settled out of court for an undisclosed sum and Smash Pictures agreed to stop any further production or promotion of the film.[207]