There is no city government, state/province. Just the parliament. PAP has had an overwhelming majority for Singapore's entire existence (helped by some rather dubious methods). If a law needs to be passed - it's passed. There is no real debate.
You need a police permit to protest in Singapore (except for Speaker's corner). Today, there is little culture of protest in Singapore. They've pretty much completely passed their reins of power to the government.
Singaporeans like to call the country Singapore Inc. And it's true. It's about as close to a business structure as one could imagine.
Considering many years later North Korea has changed very little in behavior both internally nor externally, the second part of the rumor is that the conclusion of the studies was that the Singapore model couldn’t be applied to North Korea.
1. I think the establishment of Special Economic Zones by Deng Xiaoping was inspired in part by Singapore's success.
2. Rwanda, which now seems to be doing well in an economic sense, is led by Paul Kagame, who is frequently compared to (and may even be trying to model himself on?) LKY. (Personally though, with the genocide, and Kagame's military background, and Rwanda's continued involvement in Congo, I think the analogy may actually be strained.)
3. The Brexiteers (optimistically, or delusionally), spoke for a while of trying to create a "Singapore on Thames" (London). I suspect LKY would have been amused.
The general theme is that comparisons to LKY seem to be more aspirational than truly legitimate. But the aspiration does exist.