You're gonna be bothered by how cool I am.

It's been evident ever since the Yule Brawl that Harry has thought Ron and Hermione have a thing for one another... ever since he thought that "Hermione got the point better than Ron did."

I'm really delighted that you think so! I've read so many H/Hr shippers go on about how there is absolutely no romantic implication in this scene whatsoever. But it seems as long as you tell yourself it's "just Harry's interpretation" you can see it perfectly clearly. Now you just have to take the next step and realize it's not just Harry. ;)

Ron often DENIES that that's what it is... and said "just as friends" "free agent" and Harry simply doesn't believe him!

Harry doesn't say whether he believes him. How do you know if he does? I think you mean something different than I do when you say "Harry thinks." I think you mean "the narration implies it is the case," regardless of whether Harry has any stated opinion on the matter at all.

And I have to confess - I do form my opinions on this world by actually reading the words in the books. If you want to take every single thing that's written and call it "Harry's opinion" and say the entire narrative is always suspect - and that therefore we can never know anything at all - then I don't know what to tell you. Only that I urge you to be brave instead!

Actually, she did not shoot down H/Hr... she seemed as if she was confirming R/Hr and H/G, but not once did she even mention H/Hr. She did everything BUT mention it

But H/Hr was exactly what they were talking about - it was the lead-in to her statement! Look at the context of her words: Emerson called H/Hr's delusional, and JKR said she's not going to say that, BUT "I am however, going to say..." She didn't just change the subject midstream - they were talking about the idea of shipping Harry/Hermione, and she responded with her own statement on the subject that she thought was more tactful than what Emerson said. And her more-tactful statement in response to the idea of H/Hr was "it's going to be clear once you've read book 6" and "it's done" and "it's Ron and Hermione."