I took a quick look at the paper just now. As usual, AQR approached the problem from several different angles in order to see if they'd reach the same conclusion (they did).
They only test front-month index options, though. (As far as I can tell, when they use the term equity option, they mean index option.) Long vol traders I've looked at tend to go to less expensive places to get their exposure - for example, longer dated index options, calendar spreads, individual equity options, and VIX futures three to seven months out.