disclaimer: I really don't nearly enough about this stuff to be taken seriously, these are just my immediate thoughts.
fMRI is one of the best tools we have, but that doesn't mean it's good. fMRI shit should always be taken with spoon of salt. source: a bunch of grad school friends in neuroscience and psychology a few years ago.
"on two patients whose language networks were destroyed by stroke, plus fMRI on healthy volunteers solving the same puzzles silently. Both lines of evidence point the same way: the language network sits out during reasoning." that doesn't mean they didn't learn the meta-ability of how to solve such things without language. You can learn something with language, move it to a separate "database" in some abstracted form then pull from that "database" from a non-language component. In fact I would think the language-isn't-thinking people would favor an explanation where the thinking ability is stored independently of language. I guess my point is that no "language" component being lit up during a specific reasoning task doesn't exclude the possibility we learned that specific reasoning algorithm (for lack of a better word) via language + other things.
TL;DR maybe this specific "logic" ability is a learned-via-language+ component of the brain. Language not being active during that puzzle could just mean language+ generated that component and stored it in a more abstract form than language.
What we need here, though is highly unethical, is people that were never taught language to compare to. A bunch of feral children or something like that. We do know from feral human studies that not learning language at a young age seems to make learning a lot of things nearly impossible later.
Because the system modifies itself it's going to be difficult to untangle cause and effect here.