I want to see if your hypothesis of "the AI assigns Rowling to any fic with HP characters in it" is true by bleeping those characters out.
I can't recall if My Immortal or Thirty Hs is less like the original canon, so I'll use both.
My Immortal first three chapters with HP characters (no ANs besides in-text ones): Cory Doctorow?!
Hmm. Let's try it with more material.
Same as above, except first seven chapters: Rowling.
Same as above, but the names switched in for more generic names (excluding OCs): Rowling still.
So, I don't think it's the AI auto-assigning names because of the HP Characters appearing from this evidence, but one more HP badfic to go, naturally.
Thirty H's first chapter alone (not the AN one): Rowling
Same as above, but with names genericized (except OCs): Stephen King (oh geez pffff)
Thirty H's first seven chapters: Rowling, as expected.
Same as above, but no HP names: Cory Doctorow
Conclusion: It depends on the material. If it is similar to Rowling's writing style (Both of my Mission Ones, My Immortal), then it brings up Rowling no matter the case (unless I shpxed up and left a couple of HP names in My Immortal), but if it isn't (Thirty H's), it gives a different result once the names are replaced.