Okay, so according to the timelines I have seen Kylo was in his mid-twenties when he took out the Jedi academy. Rey looked like she was 5-7 years old when she was dropped off at Jakku. Doing that math she could easily have been his daughter from an illicit affair at the academy. This solves for most of the issues I have seen floating around.
She would be young enough to not recall everything about her childhood and to have blocked out a lot of the trauma.
Kylo recognizes her and her desire to kill him, which she does, because he killed her mom and all the people she knew. It may be in the back of her head, but it is there.
She is as powerful as he is (thus Luke's comment about being as strong as Kylo)
Luke's comments about his family being force sensitive would include her.
She has some basic training from growing up a bit at the academy
She was taken away from him after the academy incident and left on a desert (mirror of Luke being hidden from vader)
Leia recognizes her after a bit (she would probably only have met her a couple times as a child)
The light saber is attuned to her because she is a skywalker
It would explain why Kylo wants her to join him not fight him.
Luke sort of recognizes her when she lands with his lightsaber. It wasn't a "who the heck are you" look he gave, more of a "I didn't expect you to find me" look.
Toss some counter points to me and I will see if I can answer them.
TLDR: They aren't skirting around the "empire = the last jedi" poetic rhyme. They are embracing it completely. "Rey, I am your father."