The single sentence of text is a single sentence of text. The system’s math supports my claim. But, of course, nobody wants to crunch the numbers to confirm for themselves, least of all people who don’t like the guideline. It is true that math is built on those assumptions, whether you believe me or not. Again though, those assumptions don’t need to be adhered to for the game to work.
Personally I usually have 5-10 encounters between long rests*, a couple other people in my game also DM and they've mentioned how much it changes the feel of the game (for the better) and that they now use it in their own game.
I find it works better to balance the different classes out, throw in a short rest or two and classes with short rest options also have a chance to shine.
*The 6-8 is medium-to-hard encounters.