I think culture and education play much bigger roles than anything else, all the sources I find show Germany and France having similar level of corruption (on top of being geographically and economically close) but completely different level of "social trust".

China's pretty corrupt politically but the social trust is quite high, the highest outside of northern europe as far as I can tell

https://ourworldindata.org/corruption

https://ourworldindata.org/trust

Kinda; authoritarism runs on bribes and nepotism, of course corruption would have lesser effect here, it's expected

It's not a tautology because it's not guaranteed. There are plenty of plausible sounding claims that fail to be true. That's why science is needed: to provide _empirical_ evidence for/against a claim.