The metaphor is not appropriate because a HOA isn't limiting competition in any meaningful or significant way.

Whether or not a couple houses in a couple block area, or 1 apartment building all "collude" to do something has very little effect on the competitive market of the massive housing industry.

But large, major players in the education space (each of which enrolls thousands of students), all agreeing together to do something, has a much larger effect, in comparison.