A garrison resource generating building is something like the trading post or the lumber mill. What a lot of people have forgotten by now is that early on you will have horrible garrison resource problems. The level 3 garrison costs 2000 resources which you are not likely to have by level 100 unless you don't play very much. Upgrading all your buildings to level 3 will also take a lot of resources.
They are very useful buildings in the begining but lose their usefulness as time goes on. The trading post has other uses but the lumber mill has a very short useful life.
That video was posted before the expansion even came out, I don't think that guy was very good at predicting what would happen on live servers. The thing is since crafting professions are time gated a level 3 mine and herb garden blow past the pitifully small number of herb/ore you need in the "cross over." Alchemy for example takes 10 blackrock ore per day, you get probably 100 or so a day from a level 3 garrison mine.
I have every single profession at max and run them all and 1 single herb garden covers all of my herb needs. Non-alch/inscription professions don't need that many herbs as mentioned above and a max level alchemist doesn't have much use for herbs either if we're being honest. Most of my herbs go to inscription but I still always have more than I can use at any given time.
Ore is the only time you will run into trouble, if you have an engineer, blacksmith, and JC a single mine can not produce enough ore for your daily needs, but, given that implies you have multiple characters it means you have access to more than 1 mine, so problem solved.