Yeah, honestly, I think you’re overanalyzing the lightsaber thing a little. Rey stole it?

Luke rejected it. Luke didn’t want it, and he obviously didn’t care that Rey had it or he would have said something. Rey even offered it back to Luke again before she left.

Honestly, I think the whole movie Rey doesn’t even think it is hers. She doesn’t think she is the hero, she is merely the custodian of this Excalibur until she finds the real hero. At first she thinks it is Luke, he rejects it twice (for a multitude of reasons). Rey even thinks Ben might be the hero later in the film, and I think she brings the lightsaber with her in hopes that he will be the one to take up the mantle. She even tosses the lightsaber to him during the battle. It isn’t until she realizes that Ben hasn’t turned back to the light does she start to accept that maybe she might need to be the hero. And clearly when Luke says he won’t be the last Jedi, referring to Rey, I think that is him being cool with Rey having the lightsaber anyway.

And sure, if you go by bloodline, Ben might have some claim to it, but I think the movie has demonstrated that bloodline isn’t the end all be all. Rey catches the lightsaber at the end of TFA because she is “pure of heart” with “noble intent”, which is what the Force really cares about. Ben doesn’t have that.

This is my own personal opinion, but I think the only reason Rey is on this journey is because she demonstrated that she is empathetic person that wants to help others, which she shows us early on in the film when she helps BB-8. I think that made her worthy in the Force’s eyes.