I think what this method is getting at is that while someone else is in the process of moving, none of the villagers will ping you to move out (for the most part, at least). This means that if a villager is moving out, most of the other pings you'd get would be non-moving pings. If the game wants to force a villager to ping, they'll have to ping you about PWPs, greetings, and other things like that because they can't ask you to move.
However, I don't think this method is actually universal. It's probably random.
I'm not sure how it's even possible to get multiple PWPs in one day since I'm pretty sure the game has a limit of one villager-request PWP per day, unless you're TTing or resetting a lot.
Even if there's a slight increase, I don't think this is worth the risk unless you're moving out a villager you want to move out. Also, saving during pings will interrupt that ping and when you reload, they won't be pinging you immediately about the same thing. The time you'd be spending reloading and getting villagers to ping over the span of days takes a lot more time than just trapping a villager of the personality type that requests the PWP you want, then being in the water for five minutes and going back to that villager. The diving method requires less active effort on your part than resetting does, because at least you can multitask while you wait for the timer to ring.
The game is programmed to have a villager PING you to move out every 4-6 days.
This isn't true. Villagers can ping you to move as frequently as every 2 days.