Rather than a binary it's much more likely that it's a mix of factors going into results that includes basic reasoning capabilities developed from the training data (much like board representations and state tracking abilities developed feeding board game moves into a toy model in Othello-GPT) as well as statistic driven autocomplete.
In fact often when I've seen GPT-4 get hung up with logic puzzle variations such as transparency, it tends to seem more like the latter is overriding the former, and changing up tokens to emoji representations or having it always repeat adjectives attached to nouns so it preserves variation context gets it over the hump to reproducible solutions (as would be expected from a network capable of reasoning) but by default it falls into the pattern of the normative cases.
For something as complex as SotA neural networks, binary sweeping statements seem rather unlikely to actually be representative...