I'm not sure I buy this explanation. How does the coffee know if the water is moving? Also, the water isn't moving in a french press, but it still brews excellent coffee.
(I think the real answer has to do with the rate of diffusion and the saturation of the coffee/water solution. Near the grounds, the saturation is higher, and that water will extract less coffee from the grounds. Move that saturated water away, and more coffee can be extracted. I guess the teabag makes that diffusion even slower, resulting in incomplete extraction.)
This limitation has traditionally made brewing coffee by the cup messy and inefficient.
I also don't buy this. Single-cup french presses and drip aperatuses are not particularly messy or inefficient. You put a spoonful of coffee in them, add boiling water, and wait. Rinse, repeat. :)
You are correct that you must "agitate" the water.. You have to stir it for a few minutes. I think it tastes better than instant coffee (which seems to have some sort of bizarre chemical taste, at least to me).