Idk if you are still reading here, nanny, but I owe you an apology for a couple of things. First, I misread the first part of your name earlier and called you, "Nancy," LOL! Sorry about that!
Second, I realize you didn't say you got involved in a parenting issue when dd and family were "having a bad day." You just said you "tried to defuse things" (or something like that, I don't have it in front of me). But whatever it was about, unfortunately, dd and her bf may have felt you overstepped, as a pp said, even though I know your intentions were good.
I'm glad you sent an email letting dd know the door is open, just in case she is in a coercive relationship. I hope somewhere in that email you apologized for your mistakes in the situation. That might go a long way to softening dd's heart if she's angry at you for any reason.
If dd lied about the advice, Imo, that was a very immature thing to do. Chances are she thought it was the best way to convince you to stay away, but I still find it immature. It's possible, as notanan says though, that the school denied things because their conversation with dd was confidential. However, I would think they would just say that, so idk. Maybe, as she also suggested, one staff member didn't know what the other said. But if dd simply lied, my guess is it was to put some teeth into her nc demand. Regardless, more hugs!