It seems difficult to me to distinguish between two explanations for their findings. (1) People who give the wrong answer to the bat-and-ball problem aren't altogether unaware that they're substituting an easier problem, after all. (2) They are altogether unaware, but explicitly asking them how sure they are about their answer triggers more reflection and then they are on some level, to some degree, aware that they've fudged it.

(Maybe there is no fact of the matter as to which of those is going on. But it seems like they ought to have different consequences, even if it's really hard to disentangle them experimentally.)