I've tried the pattern and it seems like it's also unmovable, and just doesn't feel right as texture since it's hard to change the colors and contrast of it.
No idea how to apply the nozzle
But i don't think it's what i'm looking for because the high contrast of the texture in the example, was just to show the difference between brushes.
Yes it seems that creating it on a new layer and then moving it is the only solution for it. Harder to hit the mark though.
I guess i'll just have to make better paper textures.