I'll admit that I find this discussion a bit navel-gazy. It has become a question of semantics not a question of actual functionality. The question has become "what do we mean when we use the word 'reasoning'" which is uninteresting. Dijkstra said[1] "... the question whether computers can think. The question is just as relevant and just as meaningful as the question whether submarines can swim." I don't see a clear…
Human reasoning, and intelligence, of which it is a specialized form, clearly have a biological basis that is being selected for. These aren't just nebulous words - there are some concrete biological/neural mechanisms at work here, and whether or not some "other method(s)" can provide the same, or lesser, or greater, capabilities very much depends on the specifics.
There WILL be lines of demarcation and areas of capability overlap and exclusion, but those depend on the specifics, and if the goal is to match or exceed human reasoning capabilities then understanding what those are is obviously going to help. For example if your "other methods" (artificial reasoning) are all varieties of auto-regressive prediction, and the brain is also doing something more that can't be couched as prediction, then you are ngmi!