Fair, but the same is true of me. I don't actually "reason"; I just have a set of algorithms memorized by which I propose a pattern that seems like it might match the situation, then a different pattern by which I break the situation down into smaller components and then apply patterns to those components. I keep the process up for a while. If I find a "nasty logic error" pattern match at some point in the process, I "know" I've found a "flaw in the argument" or "bug in the design".
But there's no from-first-principles method by which I developed all these patterns; it's just things that have survived the test of time when other patterns have failed me.
I don't think people are underestimating the power of LLMs to think; I just think people are overestimating the power of humans to do anything other than language prediction and sensory pattern prediction.