For this to be equivalent to the XP version, these people must be burning their way through encounters at a rate I find implausible.
Well, that's what they say! That said, I think you discount table-to-table variation.
Ignoring the first four levels (which most table do get through fairly quickly), we come to an interesting inflection point. From fourth level on, can you acquire the XP to level up in 2-3 sessions?
When I first started running 5e, using an experienced group of players and ToTM, and using standard XP rules (giving out XP for encounters- defeated through combat or other means, but usually combat), this was accurate. Because I was annoyed keeping track of that, I moved to a different system. Still, that tracked my observation at the time.
The problem is there can be a lot of table variation. Do you run tactically complex battles with minis? Are you running a session where the party is running from Tucker's Kobolds that takes multiple sessions? Do the players take frequent breaks? Are the players unfamiliar with the rules or how to play or just generally unprepared when "their turn" comes up? Is Chad on his iPhone again? CHAD??!!!
I think the more interesting way to look at it is this- if you find this implausible, but this is the recommended amount of time required to level if you are doing it in a time-based format, how does that make you feel about the games you run and the way you are doing XP? In the end, every table is different, so instead of wondering about the implausibility of the advice in the DMG, I find it best to wonder about what that means about the assumptions I am making regarding leveling in 5e (especially if I didn't read the DMG and just made assumptions from prior editions). YMMV.