Please understand, that while every good golf swing must have fundamentals to enable consistent repetitive center face contact of the golf club to the golf ball, to produce dependable results, the above is bang on!
Therefore when you hear my way is the only way, then how come on the PGA tour the above 3 individuals with completely different swing paths have such good results?. Arguably Jim Furyk in the center has the most un orthodox swing, yet is one of the best ball strikers in the history of the game, currently with 17 wins including a 58!!!
The golf swing to be consistent must use the fundamentals while utilizing the players natural bio mechanical movements. Otherwise, as I have always said the swing will break down when you have not practiced enough, when you are sick, tired, stressed etc etc. Also an unnatural swing will lead to long term injuries!
Find your swing with the coach that's right for you!