No, that's simply not true. Top salespeople routinely make more than CEOs, for example. The CEO of Japan Airlines took less total compensation than the airline's pilots did. Recently, Haruka Nishimatsu (JAL's CEO) lost pay because one of the airline's pilots was caught drunk and sentenced to 10 months in prison in the United Kingdom. JAL routinely ranks as one of the finest airlines in the world, and they've been ranked as having the world's best economy class product for three years running.
Who famously worked for $1/year in salary during his second stint. Jobs only became wealthy (or even was paid anything) when Apple's shareholders did well, and they did.
There are many issues. Labor markets do not function perfectly or even particularly well on their own, left to their own devices. Government plays a big role in supporting and regulating labor markets, including here in Singapore.
How about if voters decide ministerial compensation via direct democracy? Or, if you don't like direct democracy for some reason, how about if there's a 7 member ministerial compensation board, and voters directly elect those board members?
Ministerial salaries probably shouldn't be benchmarked to the private sector much at all, or not only to the private sector anyway. I think they should be benchmarked against what high quality, high performing, low corruption governments manage to achieve with their levels of ministerial compensation. Pick a basket of developed, small country governments that are doing well or even better than Singapore -- Switzerland and Denmark come to mind as two examples -- and benchmark against them.