[Double_A]

I think he means that checking gives your opponent the chance to bluff/semi-bluff the next street, or make a second best hand that will pay you off that normally would just fold the flop. Those 4 outs aren't quite what they seem either, since you have a pretty huge redraw against them. So while you may give up something the times that your opponent spikes his 4 outter and you don't hit your 12 outter on the river, you make more than when your opponent bluffs the turn, or makes a second best hand that he normally would have folded on the flop.

Of course, if your opponent will peel on a board like this with most of his hands, or is overaggressive with his bluff check/raises, it is better to just bet the flop.