It takes a leap of faith but learning grammar almost exclusively through example sentences is actually really efficient.
Krashen, Khatzumoto, Matt vs. Japan, and Antimoon are all worth reading if you want to go down this rabbit hole.
How you absorb the grammar of a language is a separate question from when you should do conversations though.
Some folks advocate conversation day one, but most pro-input folks do recommend waiting until you have a sense of how things work and can make fewer mistakes.
EDIT: One of the best articles explaining this anti-rule view: http://www.antimoon.com/how/input-gramrules.htm
Definitely seems to be the case in machine learning. Flexible models trained on huge amounts of data beat older hand tuned grammar rule models every time.
With that said I still find GP's complaint pretty weird, since TFA strikes me as being in the "beginning stuff that even advocates of input learning would teach out of a book" category.
I mean, if I was teaching somebody Japanese then I'd probably cover how particles work on the first day. Surely only a madman would expect someone to absorb that organically.
Passed JLPT1 after a couple of years, and had the time of my life learning Japanese. Particles are the glue that holds it all together but they are deceptively simple on the surface with an ocean of complexity lying underneath.
I don't think TFA is claiming to be the only thing anyone needs to reach fluency. It's clearly just meant to be a learning aid. Unless you believe it's counterproductive, and that lists like that actually make it harder to learn a language, then I don't understand the complaint here.
You can make yourself understood using simple sentences and botched grammar, if the key words in them are the right ones.
You can't even study grammar without vocabulary, because grammar study uses examples. Examples loaded with words you don't understand are poorly conducive to learning.
The best resources for Japanese grammar assume that you can read. You get some furigana over some of the kanji and that's it.