What is missing from the anecdotes is that all of those players with wonky swings or strokes like Trevino, some bowler, etc. did nothing but play their sport for their entire lives. They had the time to perfect whatever method they used and made it work somehow. But even Michael Jordan said that the difference between the good players and the great ones is fundamentals, and that's among pro level players. How many Trevino's are out there who couldn't make it because they couldn't groove a bad swing?
Mere mortals who play pool as a serious hobby need all the help they can get. Using good fundamentals is important. The problem is nobody in pool can seem to agree on exactly what those fundamentals are so we say "whatever works for you." I think reality is somewhere in the middle. Players can have their own individual style but there must be certain fundamentals that every good player follows.
Seems like snooker players are in agreement on the fundamentals for the most part from what I can tell.