That seems to imply that the multiplier should not be used for calculating the difficulty of the encounter either.
In order for this to be relevant, I guess you have to be assuming that numbers affect difficulty for combat, but not for other interactions? Assuming that it is, fundamentally, an adversarial interaction, and since this is all very rough approximation anyway, combat difficulty seems like a reasonable stand-in even if things are resolved without physical violence. It represents the general threat that the adversary poses.
Absolutely, it depends.
For a group without area effects, particularly a group below 5th level, yeah the XP multiplier guidelines in the DMG make sense: A fight with more monsters is more challenging, but also something you want to avoid if possible.
For a group of skilled players swimming in area effects, particularly a group above 5th level, the XP multiplier guidelines in the DMG may not make sense.
Part of the art of DMing is figuring out the sweet spot for one's group. I've noticed myself doing a lot of impromptu "gauging the wind speed with my thumb" to determine how difficult an encounter might be. Here's a recent example...
In my Al-Qadim game, I ran a homebrew seven-headed Pyrohydra (CR 13) against a party of six 11th level PCs. It would be a "medium" difficulty encounter for a party of five PCs, but for six PCs it was just an "easy" encounter. The PCs had a bunch of NPC support, however none of that came into play because the pyrohydra surprised the PCs and their allies (who had low initiative scores). In fact, two of the PCs were surprised as well, and all the PCs' allies did was soak up a few attacks and put their pack animals at risk. And the pyrohydra was fighting from the water, and I gave it some spontaneous abilities like a reactive tail slap & the ability to use its fire breath to make the oasis pond it lurked in begin to boil.
Overall, the outcome matched my expectation: an "easy" encounter, which I intended to set the scene, get the party asking questions, and give them a long overdue fight. However, my small tweaks made it more interesting than a "throwaway" or "boring" easy encounter.
Personally, I found using the hydra to be a good litmus test for a party's capabilities when it comes to multi-attacking (rather than area effect attacks, which are pretty obvious). It has a lot of attacks, simulating an encounter with a # of monsters = to its # of heads, but it goes down faster.