Do we always want opponent to make FTOP mistake?

[electrical]

It's been a while since I've read TOP, but this has been bugging me since an example came up in a discussion elsewhere.

Imagine you are in an evenly-matched stud game. You have (JJ)K, and there are several limpers with lower up-cards. A Queen to your immediate right completes, and you raise. One other player calls and the Queen calls.

On Fourth street, the little-card limper immediately to your left catches an Ace, you catch a Ten and the Queen catches a Six. The Ace checks, and the action is on the Queen. If the Queen has a pair of Queens, his best play would be to bet, hoping we re-raise to force the Ace-little guy to fold. If the pair of Queens knew his hand was best, he would certainly bet, and not doing so is a FTOP mistake.

It is a FTOP mistake for the pair of Queens to check, but it is worse for us if he makes this mistake. We would prefer him to bet so we could raise to force out the Ace-little guy and increase our chance of winning with two pair.

According to the wording of FTOP, we "profit" when he makes a FTOP mistake. How does this apply in this instance?