To me this is more an approach that varies greatly between different players and likely heavily influenced by experience.It is a rule, but it's easier and more often changed than other rules. Here's the fluff for a cleric, "Divine magic, as the name suggests, is the power of the gods, flowing from them into the world. Clerics
are conduits for that power, manifesting it as miraculous effects." Unless the DM changes it, that is what a cleric is. A divine caster who is a conduit for the power of his god. That's as strong as any rule in the book. Sometimes fluff is less restrictive and gives you options, like some rules are less restrictive than others and give you options.
Rules do not have to be mechanical in nature. Over the years it seems like a lot of people have forgotten that fact. They argue as if unless something is mechanical in nature, it can't be a rule.
I think players who have played a lot more "universal multi-genre" point by games like HERO abd some indie etc. but there are plenty tend to be more along the mindset of separate mechanics rules and setting dials. Others who either did not play a lot of those or did and found it wanting i think are more likely to find it more to there liking to have clerics required to deal with npc church and divinity or warlocks not to "follower" or "minionize" their patrons to the role of off-screen sfx.
I do not think either is bad as long as its universally agreed at a table and implemented well.
However, DnD does not present itself as a generic separation between mechanics and fluff system but as a married setting to mechanics with alot of homebrew enabled.