The important point to remember here is that this decision only affects the multiplier on the encounter to determine how difficult it is. Therefore the points to note are:
- This is a "rule of thumb" calculation in the first place. A "Hard" encounter is a very broad area and (despite what the table with its hard boundary suggests) it merges into "Moderate" at one end and "Deadly" at the other.
- It has no impact on the XP the PCs gain in the encounter.
- It is primarily a decision about encounter "pacing" or how many encounters the PCs have before needing to rest. You have way more direct control over this by e.g. bringing an encounter forward if the PCs are flush or deferring one if they are lean on resources.
Therefore it is primarily a judgement call that does not have huge implications. To illustrate consider the examples that you have given:
CR3 Mummy plus (3) CR 1/2 Swarms of Beetles
XP = 700 + 3 x 100 = 1000
Multiplier: 1 or 2 giving 1000 or 2000
CR3 Goblin plus CR1 Lieutenant plus (5) CR 1/4 Swarms of Beetles
XP = 700 + 200 + 5 x 50 = 1050
Multiplier: 1 or 1.5 or 2.5 giving 1050 or 1575 or 2625.
Against say 4 Level 3 PCs, in both cases the first multiplier rates this as "Hard" and any of the others are "Deadly" - what this says is that these are dangerous encounters; be careful. The low CR creatures will have a significant impact on the fight. So using them in the multiplier is reasonable because they low CR creatures will use up significantly more of the party's resources.
Against say 4 level 6 PCs, they are "Easy" to "Medium"; but the low CR creatures will probably be rendered hors de combat in Round 1 - their only contribution is to distract the PCs for that round and maybe burn a fireball. Not using the multiplier would be reasonable here because said fireball will probably be damaging the main protagonist as well so there is no additional drain on party resources.
CR10 and CR1
XP = 5900 + 200 = 6100
Multiplier: 1 or 1.5 giving 6100 or 9150.
This is a deadly encounter for the parties above with the first guy alone (and a probable TPK for the L3 guys).
For 4 level 10 PCs its "Medium" without the multiplier and "Hard" with it. However, given that the CR1 monster can probably be dropped with a Cantrip (3d10), Single attack or at most a 1st level spell (Sleep) it doesn't really add to the difficulty - he will distract 1 of the 4 PCs for part of 1 round. Ignore it.
How is this difference reconciled? Is there something I missed about Nimble Escape?
It isn't. No.
It has been said before on this site (but damned if I can find it) that the CR of the monsters in the Monster Manual were not set using the methodology set forth in the Dungeon Master's Guide - there were established by eyeballing and playtest.
Notwithstanding, the DMG does say (p. 237):
Creating a monster isn't just a number-crunching exercise. The guidelines in this chapter can help you create monsters, but the only way to know whether a monster is fun is to playtest it. After seeing your monster in action, you might want to adjust the challenge rating up or down based on your experiences.
See Ogre CR calculation: is it wrong or am I missing something? for a calculation that goes the other way.
Think of the CR calculation as trying to work out how to fly a spacecraft to the moon with calculations on the back of a napkin.
Best Answer
Neither and both.
Unlike in Previous editions, CR isn't used to directly create combat encounters, instead the XP values of the creatures ( which is tied directly to CR) is used to determine how many creatures can be used in the encounter. Instead, CR tells you the upper maximum difficulty of the monster, assuming a party of 4. One of the reasons why they moved away from using Level instead of CR, is so that you did not confuse the CR of the Monster with the level of the characters fighting the monster.
So, basically a CR1 monser means that if your characters are level 1, this will be a challenge for them. If they are level 2, it will be pretty easy depending on how you use the xp budget to put 1 or more monsters into the battle. If the monster is CR 1/4, then that means that if you have a single character alone, without the party it will be a challenge for them, 1/8 means 2 will be a challenge for an indvidual, and a CR 0 means it's not a challenge for anybody. You will notice that CR 1/8th has an XP value of 25 while a CR 0 has an xp value of 10.
But the important criteria you want to use when buliding an encounter is your XP budget. Use CR to only filter out which creatures are too deadly for the level of your party of any size.
Challenge Rating, page 56
When building encounters, use XP values. Those XP values along with the relevant multipliers for party size and number of monsters, are what are important when determining how deadly a monster is to the party or to a character. CR is only a filter for the "upper limit" of which monsters you should choose from when using the XP budgets.
So in the end, trying to understand how many party members a CR is coordinated against, becomes a bit of a red herring for when it matters. The answer is "4", but that isn't really the answer you want, what you want to focus on is your XP budget, and the multipliers for party size and number of monsters.