That assertion feels suspiciously like a logical fallacy.

Not really. If the solution has less complexity than is inherent in the problem, it can't possibly work. If the solution has complexity equal to or greater than the complexity inherent in the problem, it may work. So if you see complex code handling many different edge cases, you can take that as an indicator the author understood the problem. That doesn't mean they do understand or that the solution does work; only that you have more confidence than you did initially.

It's a weak signal but the reasoning is sound.

Everything should be made as simple as possible, but not simpler.

Code has a minimum complexity to solve the problem

Not really. A different place to look for this is in chemical reactions and things biological life does.

You may have some simple chemical life needs, and life may have some other simple chemical it can use to get the needed simple chemical, but the processing steps are complex and limited by physics themselves. Evolution almost always finds a path of using the minimum activation energy to let these reactions occur. Trying to make the process simpler just doesn't get you what you need.