The problem with your idea is that it makes things incredibly murky imo. Rey isn’t even revealed to be a Palpatine until the tail end of the hangar scene, so why should it even be mentioned there that Palpatine intended to lie about her being one there if Kylo immediately shuts it down in the next sentence? When Palpatine later starts his whole “Empress Palpatine” spiel, all Rey has to say is: “Nah, Kylo and Luke told me that’s false. Besides, Leia has always been more accepting of me. Look, I brought these two lightsabers with me that she gifted to me, why don’t you just start shooting some lightning at me so I can reflect it back at you?”
The problem with Rey Nobody is that it benefited the narrative of TLJ, but runs counterintuitive to the dilemma of Rey striking down Palpatine to take the Sith throne. Allow me to explain. If Rey is a nobody, that means she is free to make her own legacy. She gets to decide how to go forward from there with absolutely no restrictions whatsoever. That’s what makes Kylo’s offer so enticing to her in TLJ - they get to make something new together. Confronted with striking down Palpatine, if she’s a nobody, the only thing he can offer her is a sense of belonging - with the shadowy cloaked figures watching them whom she’s never met in her life. In this scenario, Rey is just coming out of a conversation with Luke about how Leia has so much faith in her that she wants her to carry on her Jedi path. The only thing that could shake that foundation just a bit is if Rey is related to him, or the stronger of the two, Rey was literally created from a vat to sit on that throne and is a clone of Palpatine. Adopted by nobody parents to rescue her, only to be later adopted by the Skywalkers.
Now, yes, Rey being a chosen one who determines the fate of the galaxy - Vader or Anakin style - would allow her to be a nobody and still have some semblance of temptation. The problem with that idea is you have to cut out so much of the conversation between Rey and Palpatine (among other things), and I remain unconvinced that any of this would feel natural in a movie with such rushed pacing as it stands. The conversation between her and Luke on Ahch-To, for instance, wouldn’t have a lot going on because it would have to remove “some things [being] stronger than blood” and Leia seeing her spirit and heart to counteract something negative about her.