It's basically a specialization of the base rate fallacy. If, say, idiots can still be right by chance 10% of the time, and experts are right 90% of the time, but only 10% of the population are experts, then lucky idiots will make up fully half of the population of people who are right.
10% is pretty generous for most of the work experts actually do, though.
Experts do many things, one of which is to occasionally make predictions, where 10% might be more reasonable.
But, for work like imagining how a given goal can be realized, I would guess an "idiot" could compose an achievable plan less than a fraction of a percent of the time.
It's all about having enough variables in the system so you can point to something else as the cause when there is failure, and yourself as the cause when there is success. With willful ignorance of reality, idiots can have a success rate much higher than 10%. :)
