I heard the same story when I was a kid, but it was about a boilermaker. The rest was for knowing where to tap his hammer to fix their problem.
It's an obviously apocryphal story with two great messages. First, don't undervalue your expertise just because the fix was easy (I still have a problem with that). Second, if you don't know what you're doing don't question the expert just because it looked easy.
I know a version with a graphics designer. They designed something in 10 minutes and asked 1000 USD for it. When confronted on why it is so expensive for just 10 minutes of work, the answer is that it's not just the 10 minutes of work, but also the 10 years of experience that lead to this 10 minutes of work.
At the beginning of the 20th century Henry Ford's electrical engineers had issues they could not solve with a gigantic generator. Henry Ford called Steimmetz, a genius mathematician working for GE to help them.
When he arrive at the factory he spent 2 days and night listening to the generator and scribbling on his notebook.
After that he asked for a ladder, climbed on it, put a chalk mark on a specific spot and explain to the engineers that they needed to remove the plate and replace sixteen windings behind the plate. After that the generator worked perfectly and Ford received a $10 000 bill.
Ford asked for an itemized bill and Steinmetz sent this
It's funny reading this, because the way I heard the story was as a railroad story.
The train engine wouldn't run. The expert was called, he arrived, and after inspecting the train engine, knew exactly were to apply a little bit of oil to make it run again. His bill was challenged as being overly expensive, and he countered with them paying for the knowledge of where to apply to oil, not the oil itself.
There's like all these different versions of the same philosophy of the story