I think it is only rumors and no one really knows the exact amount of Bitcoin that Satoshi Nakamoto has, that one million prices of Bitcoin is only a rumor and there is no solid proof about that. I guess most of the people think that he owns a lot of Bitcoin it could be true or not and he is the only one who knows about that information.
it is not rumor, it is an estimation which is more like a guess. there is a difference between the two. a rumor is usually bullshit and doesn't have any facts behind it but an estimation is based on at least some facts.
of course there is no solid proof since bitcoin provides a good level of privacy although it is not anonymous but the estimation is based on some facts such as the time he was mining solo and the interactions he had and some other things that you can read in those links.