Someone used an example from a next playtest packet earlier that makes a good example of this where they said words along the lines of "so you spend a couple days tracking the orcs through the forest" only to have the players assume long rest & get frustrated when they were told no. It makes no sense for the PCs & orcs they are chasing to not go to sleep at night during those couple days but lowering the bar for full & complete recovery of any & all things to a mere scene transition only results in bludgeoning the GM if they say no.
Of course they did. DMs who want to gatekeep Rest are fighting decades of published RAW to implement a house rule.
Go read the 5e PHB: there is nothing there about Rests being something DMs need to give permission. "Adventurers, as well as other creatures,
can take short rests in the midst of a day and a long rest to end it." (Emphasis mine)
No caveats, unlike the skill section which says things like "Sometimes, the DM might ask for an ability check using a specific skill". Matter of fact, the term "DM" doesn't appear
at all in the section on Resting in the PHB. Resting is an event players choose to do.
A DM can interrupt it with combat or the like but there is nothing there that says they can deny it outright. Nor should they as it is based on sleeping and sleeping is akin to breathing; its a given fact of life.
DM: "make a con check to see if you pass out from oxygen loss"
Player:"I'm not underwater, why can't I just breathe?!?"
DM: "Look, I said you can breathe after this fight. Now make a Con check to see if you pass out."
And that wasn't something new in 5e. If you go back to 2000, in 3e/d20 healing merely required "a full night’s rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night."
Spell prep was essentially identical with "a wizard must first sleep for 8 hours....she must refrain from movement, combat, spellcasting, skill use, conversation, or any other fairly demanding physical or mental task during the rest period"
Again, absolutely no mention of DM permission, but there was caveats for interruptions.
DMs who want to control rest/recovery have to understand they are wanting a house rule that is at odds with 20+ years of RAW, significantly impacts game play in a way at odds with default player expectations and may indicate that they really don't want to play the kind of game that d&d has been for 22 years.
An argument for slower 3e-ish healing could be made (I personally dislike one-night healing combined with short rest healing) but totally gating of recovery beggars rationality. Even if some kind of "minimum comfort" was required by RAW (which it isn't) or common sense (which I support), 5e is a game where a 3rd level spell (that doesn't even need to expend a spell slot) can deal with extreme heat, cold, humidity, weather, and biting insects for up to 9 characters, which accounts for 99% of environmental factors that impact rest.