The news was 90% of Chinese billionaires are actually kids of government officials. That would be like if the billionaires in the UK were children of parliamentary officials or if the billionaires in the USA were children of senators and representatives. It's wrong to equivocate the Chinese situation with simply having "connections." It's a fundamental structural difference between China and "western societies."
Also, what you're implying in the weak sense is probably wrong. Billionaire lists are easily found on the internet and if you look at the bios of the people on such lists, I would assert the opposite - most of the billionaires in western countries started out with few significant connections at all.
There's a difference in degree here too though: there's a massive difference between "son of a lawyer" and "son of a central committee member". Gates is considered one of the more privileged billionaires, because his mother was on the board of directors for United Way and his father was a prominent lawyer. That seems like a crack down from his parents being President or in the Cabinet.
It also ignores counterexamples like Steve Jobs (from a working class, blue collar family), Larry Ellison (Jewish immigrants who worked as modest government employees) or Larry Page and Sergey Brin (children of professors).
Hm well professor is not exactly middle class either... Actually children of professors are probably the best prepared to make a great career more than anyone else. Parents with connections, lots of knowledge and more time than people working in the industry - that's the perfect mix. I know a few sons of professors, they just surf through life.
Buffet's father wasn't a politician until after Buffet was rich. If anything, in western countries it's easier to become a government official because you're related to someone rich than it is to get rich because you're the kid of a government official.
Also, what you're implying in the weak sense is probably wrong. Billionaire lists are easily found on the internet and if you look at the bios of the people on such lists, I would assert the opposite - most of the billionaires in western countries started out with few significant connections at all.