It's weakly linked to XP, not strongly linked. It can give you a baseline of XP to start with, and then XP is adjusted based on numerous factors (so many it took pages to detail them all). It's in no way your primary tool to judge or adjust encounter difficulty. There is a reason the entire many-page encounter difficulty section of the DMG only mentions CR in passing in a side-bar.
If a person actually knows how CR is used in 5e from having read the section, and continues to post about CR as being the issue with encounter difficulty, then they're being intentionally deceptive. But I think it's far more likely the people doing it simply have not read the DMG section on encounter difficulty, and are assuming what CR means. The disinformation might also be sourced to the free Basic DM section, which I know at one time was inaccurate (and maybe it still is - I have not checked).
I don't think this ("weakly linked") is true. They are 1:1 coupled. DMG guidelines include adjusting the effective HP/damage in order to adjust the CR, and also include abilities where you adjust the output CR directly. Then you calculate XP from that CR--just like in AD&D. Can you find a single example of a monster whose CR and XP value don't match?
Another left-over assumption: that there is supposed to be one encounter per long rest.
A "deadly" encounter that turns not-so-deadly is largely because the party is nova-ing, spending their most precious and powerful resources to curb the deadliness.
In my experience, this observation is not true. A deadly encounter that turns out not-so-deadly is because the party manipulates the tactical situation to expend fewer resources. Sometimes this means that the difficulty gets brought down to the point that the party still has to expend resources to triumph, but sometimes the deadly encounter is trivialized (via surprise or mobility) to the point where the party expends nothing but a few arrows and first- or second-level spell slots. I've never yet had a case where I made a party fight two deadlydeadly encounters in one day (my evil brain here says, "Hmmmm, from a pacing standpoing that sounds like fun" and now begins to construct plausible scenarios) but usually the main resource expended is tempo, which is infinitely rechargeable.
For example, I had a party of four 4th level and one 3rd level character raid a hobgoblin base for war plans and accidentally stumble on the hobgoblin warlord and staff (CR 10-ish; 6400 XP which is approximately
Deadly x3) instead of on the plans. Due to entry tactics they achieved surprise and got to control the initial conditions, which let them ensure that the fight occurred in a narrow corridor 5' wide, which let them ensure that the hobgoblin warlord didn't get martial advantage, which went most of the way toward ensuring that not many HP were lost in the killing of all the leadership. A Web spell from the 3rd level wizard was also expended, as well as both beast shapes from the moon druid (who was on duty against everyone
except the warlord, ensuring that no one could run off down the tunnels to get help) and possibly-but-not-necessarily some HP from the tank (who spent most of his time Dodging while the sniper shot the warlord full of arrows and the bard mocked him to death). After that fight the party declared "mission accomplished" and scrammed (after rummaging quickly through the warlord's paperwork and also casting some Disguise Selfs), not because all their resources had been expended (they hadn't been) but because they were afraid their
surprise had been expended and they didn't want to wind up fighting a whole base full of 80 hobgoblins with armor on and bows in their hands.
Come to think of it, I believe the party had actually expended more resources on intelligence and stealth than they expended tactically in the fight with the hobgoblin. One of the main reasons they were so nervous during the exit, I believe, was that the druid was low on Pass Without Trace spells. I can't remember if he was fresh out or not, but the concern was that if all 80 hobgoblins did catch on to the intruders, they might not be able to disengage successfully.
TLDR; if a single Deadly encounter leaves you so weak that you'd be unable to beat multiple Medium threats, you are (in my opinion) doing it wrong.