[Catt]

Maybe I am misintrepreting the OP's post. He is considering whether to bet or check through the turn. I think it is implicit in his post that if he checks he gets a free card. The reason he's considering taking the free card is because there is a significant likelihood that he doesn't have the best hand and fears a C/R - he may have the best hand and he may not, but he certainly believes he has outs to the best hand if he is in fact behind Villain. He would have the odds to call a bet from Villain (with his outs) given the pot size, but Villain has checked the action to him. His working approach to help him determine whether to bet or check rests on how often he has second-best hand and what if any fold equity he has against a better hand or a hand that has correct odds to call the bet when he is ahead, and the likelihood that he is C/R'd and has to put two bets in on the turn. His decision is to bet (hoping for an incorrect fold or an incorrect call, but accepting a correct call from Villain) and risk being C/R'd, or to check through and see the river.

And maybe I misintrepreted ZenMusician's post, too: but having the odds to call (say you have a draw to the nut flush) doesn't mean you bet the turn when checked to. You might if you determined that your fold equity was significant enough, but you're rarely betting a draw on the turn when you believe Villain has a made hand.