But anyway, why would the second player provoke mutual defection?

In my formulation, it doesn't have a choice. Whether or not it does exact simulation of the first player is determined by its "mathematical intuition subroutine", which I treated as a black box. If that module does an exact simulation, then mutual defection is the result. So this also ties in with my lack of understanding regarding logical uncertainty. If we don't treat the thing that reasons about logical uncertainty as a black box, what should we do?

ETA: Sometimes exact simulation clearly is appropriate, for example in rock-paper-scissors.