Paying off politicians in the US is illegal and it is prosecuted. As I mentioned, money buys you undue influence over politicians in the US - but that's true in every country. There is no reason to think the US is more corrupt than most countries, or the most corrupt in the world - as you've said. What evidence there is shows that US has unusually low levels of corruption relative to the other countries in the world.
The Transparency International index is based off of a survey of residents asking questions about perceived corruption. Paying off politicians, even if it were done as legal campaign contributions, would contribute to perceived corruption.
I know about the Peter Thiel example not because there was a massive outcry, I have basically no exposure to New Zealand news, but because I read about Peter Thiel and came across the story that way. I have no doubt that all I'd have to do to find an unending stream of money influencing New Zealand politicians is go to Google and search for it. But, I don't need to, because I already know that money is a corrupting influence worldwide - not just in the US.