"Dyche Fit" is another media-driven thing and has nothing to do with physical fitness at all.
Sean requires players to buy into his methods for keeping Burnley Football Club in the Premier League, something which, in spite of the limited resources that have been available, he has proved to be pretty good.
It is very much a mental process which players need to get into their psyche and once they are perceived to have understood exactly what is required then they will be very much part of the squad.
Some players and a lot of fans won't buy into this philosophy, however, it is not their job or pride which is on the line.

Lots of fans think that it is time for change, just as fans at Bolton, Blackburn, Newcastle and Sunderland thought with Sam Allardyce. They all lost stability and it is a long, hard process to get back. Newcastle are the exception because they have the much maligned Mike Ashley as an owner and he has kept that club afloat, no matter what their fans think.