...they're only thinking of the stereotype version where daddy hands him everything.
What's more important is the (big) leg up they get: education with minimal or no debt, some means of support (for Mitt, the stocks from his dad he was selling off to pay living expenses while in school), where they go to school, the connections they make and those they have via association with their father (the main reason W kept failing upward), etc. Even the simple knowledge there is a fall-back position if things go really badly -- you may have to go begging to daddy, but that usually beats becoming homeless.
There's a Saudi prince who occasionally gets coverage for being a "self made" billionaire because most of his fortune was made through financial ventures and not from what his family and inheritance. But that coverage always ignores that the family money is what gave him the stack to play that game in the first place. They also ignore that he's a goddamn Prince of Saudi Arabia! That means people take his calls, people bring deals to him, and anyone trying to curry favor with Saudi royalty will come to him AND make sure HE gets a good return, even if other people have to get screwed to do it.