Neo's powers are only based on the fact that in the Matrix the laws of gravity and physiscs can be bent and some can be broken taht is the only reason for his powers. Um, the Matrix rebels don't exactly know everything about the Matrix. Like what the Architect told Neo. Like they were surprised that Neo just disappeared when going through the hallway with Seraph and all the doors the Keymaker helped them through. Therefore, I don't think it'd be too unreasonable to assume that they don't know everything about what being the One entails. I think if Neo truly were the One, he'd have to destroy the Matrix from the outside, where it was created, in the real world, and while he does have awesome powers inside the Matrix, I'd find it completely plausible that his One status allows him to destroy them in the real world too, without it necessarily being a second Matrix.