Well, his story lines up with what she already knows. Carlisle even called her 'Ms. Prochainezo' when they first met.

Still. As far as she is concerned, the 'Rey' that those two know is a completely different person. She isn't obligated to take on the responsibilities of this other Rey that exists in some other universe. Especially when that entails being some kid's mother.

"Apologies. Don't remember any of those things. Am not your family. Wouldn't wish that on anyone, anyway."

Rey had been pretty clear to Nick about what being family entails to her. How she has a track record for hurting them. No one should willingly want that.