Nothing intrinsically more or less direct about the LLM's method than ours.
In my mind general intelligence is pretty much by definition a virtual machine, so the mechanisms behind thought are only relevant for the sake of efficiency (ie you can argue that LLMs make a poor basis for intelligence because tokens and natural language are a poor way to encode the world, but if you can run it on a big enough computer to counteract the inherent wasteful virtualisation then who really cares how it works under the hood?)
I will stop here before our analogies go too far.
I've never tried it and it might take some thought and effort to conduct an experiment to find out properly, but I would be interested in the answer.
"Count the 'r's in the string 'raspberry'" is the same as "Count the joints in the Tasmanian sand spider": it means, "can you instance in idea and assess it and perform procedures over it - for example, can you count?".
We want to be sure it can count. We have seen it may guess, it may construe, it may recall - we instead demand it checks. We cannot trust it without that.