Sure that’s one example but I think there’s various things like this. You have to make sure that investigators can also be made undercover where makes sense (if it’s possible to obfuscate malfeasance) and rotate the inspector’s physical location (to avoid potential for corruption due to personal relationships). You always still have other corruption vectors (eg getting buddy buddy with the inspector’s boss and influencing them indirectly). It’s an unsolved problem but you can always do better than nothing.

Under what basis do you have to claim those "random" inspections "work very well"

Personally I believe they do almost nothing. Food born illness is pretty common and almost impossible to trace unless it is a wide spread outbreak.

Many cities only inspect a food establishment every 2-3 years and in some cases as long as 5 years.

I think reputation, and economics play a larger factor in safety then government inspections. Dirty places making their customers ill tend to close long before the government inspectors come around.