Battier was an obvious rental, so Perk would have been too much. The trade for Green was a move made with the future beyond that season in mind, since Ainge seemed to feel pretty clearly that Perkins would leave in free agency.
So, imagine that the league doesn't void the trade of Chris Paul to the Lakers and the Clippers pick ends up being 11th (and it was top-ten protected, I believe). The next few players drafted who were available at that point are Meyers Leonard, Jeremy Lamb, Kendall Marshall, John Henson, and Marice Harkness. Now imagine that the Celtics could have used their own first pick to move up (so no Sullinger). The players drafted in those slots were Austin Rivers (ugh) and Andre Drummond (not ugh).