Probably yes, but still they have your information when you wi big money. And when say information, that would include where to find you and your winnings. I know these are reputable gambling sites but i don't find it comfortable giving out my private information especially after winning a big amount.
Why do you think they should find you even you win that kind of amount? Is there any news that someone that won a lot was harassed by someone that is part of that gambling site? If there's none, there's no worrying on gambling on a trusted gambling site.