Wow, I had to look that up. Apparently 2 things are happening:
1. PE firms are buying up HOA management companies, increasing prices and reducing quality of service; and
2. PE firms buy up a majority of homes in a development, use their votes to install their employees in a majority of seats on the HOA board, then dictate whatever terms they want.
Of these, I think #2 is more insidious as they can raise dues/assessments at their leisure and effectively force homeowners to sell out to avoid (or pay off) the fees and assessments. This tactic decreases marketability of the homes (b/c who in the hell would want to move into a place like this) so sellers are motivated to sell out to the PE firm when they extend an offer. Then the PE firm gets more votes...