If she had her mind altered like Revan her being dropped on Jakku as a child could be a false memory meaning she only got dropped off there once.
That leads to my second point: Her whole backstory as we know it is a lie, which I’d rather not have, as it’s removing backstory for the sake of having a twist, rather than adding to the plot.
All we know about Rey is that she was presumably left on Jakku as a child under the “care” of Unkar Plutt. That’s hardly a backstory; it’s only a notch above a premise for a backstory. Also couldn’t you say that about the “No, I am your father” twist? Furthermore, I am of the opinion that both twists would add to the plot significantly.
I’m not of that opinion, because you’re not changing her interactions and relations. She’d still hate Kylo Ren, she’d still barely know Luke (Even if she did know him once upon a time), and she still needs to be trained. Nothing has changed about her connection to anyone, except that she’s now a former Jedi apprentice rather than a scrapyard scavenger.
“I am your father,” while it did alter the backstory, it worked for a couple of reasons. The big one, though, was that it completely changed the dynamic between Darth Vader and Luke Skywalker. Before their confrontation at Bespin, Luke was raring to fight Vader; he wanted revenge for the Death of his father. After the revelation, Luke became hesitant to fight Vader; he didn’t want to be the one to kill his father, even though everyone else was practically begging for him to do so. If he was still raring to kill Vader, it wouldn’t be nearly as impactful as it we know it is now.
It can work, but I currently don’t see a matrix style “Your life is a lie” twist changing everything just yet.