I wanted to chime in and say NTA. A majority of the people here are taking you saying she can't go as being controlling, but imo, it's not. Saying "can't" is much more different "won't". If you had said you wouldn't let her go, then you would be an asshole. If you had physically barred her from going through the door, you would be an asshole. If you had followed her to the restuarant, then possibly confronted her boss when it turned out you were right, you would be an asshole. But you didn't do any of that, other than expressing your opinion through the word "can't".
Even more so, people are expecting absolute perfection during moments of high tensions. That's a common trend with this subreddit, as if everyone has perfect composure during an argument. Granted, "can't" wasn't the best word to use, depending on your relationship, bit it definitely isn't in any way controlling.
I would say your fiance is TA in this situation, especially with her behaviour afterwards. I get that she's angry that she didn't analyze the situation correctly, but she had no right to take it out on you and incorrectly call you controlling. I think you need to both sit down and talk things out and that you personally need to evaluate your relationship. Not saying break off the engagement or end things, but this behaviour is a bit intense for a supposed grown woman.
I just think it's a bit weird, honestly, that she's in HR and didn't recognize these signs. How is she supposed to be a valuable member if she couldn't even see for herself that the situation was weird. She seems to be completely in denial and needs to report her boss or even find another job, because this situation is going to blow up, either with the second girl or the boss.