I won't debate on what was "highly exaggerated" since I wasn't there, but no it isn't right for HR to do that. IMO, they should have talked to you first before letting charges go through and worst case scenario (if they actually thought you were stalking her) warn you to stop first and see if you comply.

But let me give you another hypothetical case that could have happened here. J is upset. She thinks you're stalking her and she's worried. (Which obviously in your mind you weren't, but she could still think it.) She goes to talk to someone at your school who she thinks can help her to get you to stop. (If it's serious in her mind, it's completely plausible she wouldn't confront you directly for fear of your reaction. Direct confrontation isn't usually how females handle social problems.) So now she's talking HR or investigators, whoever, and she has to put into words something that her gut is telling her. She's uncomfortable and she knows it's because of you, but more that she's afraid of you and what you'll do, but she doesn't quite know why. It's so hard to describe a hunch correctly, and HR is trying to pull info from her and she's nervous. If she uses the wrong word even once, HR gets a completely different picture from there, and encourages her to press charges in order to "keep her safe", which I'm sure they've seen a girl who wasn't kept safe before. They scare her with vague ideas of what you could do (yes, even though they know nothing about you and what you would or would not do.) and she agrees to go forward and have someone "talk to you", which they turn into an investigation. It spirals from there into a year long problem, where she has to keep describing a gut feeling that she had, but probably can't quite put into words accurately. You view it as exaggeration, to her it's self preservation.