This doesn't seem true and I'd be interested in any stats that back this up. It reminds me of a very interesting result (that most never internalize) which is that the number one way to avoid corruption is to pay public servants handsomely such that the job rivals the private sphere. Most developing countries can't do that, and that's why most of them have issues with corruption.
Rich countries also have crab-bucket like behavior. You don't have to look twice at the current US administration to see lots of corruption and cheating and fraud, for example.