More (not so) fun facts:
54% of American adults read below a 6th grade level.
21% read below a 5th grade level, which is considered functionally illiterate.
High immigration numbers don't fully explain it either, as first gen immigrants only make up about 1/3 of those with low literacy.
I'm saying that just because something is specifically intended for something doesn't imply that it has a larger effect than other things which have broad effects.
So no, the fact that homeopathy is psudoscience is irrelevant for my example (and the argument as you phrased it above). I read you, effectively, as saying:
because teaching is intended to influence literacy, and poverty reduction influences many things, teaching has a bigger effect