No. You are confusing the model for the reality. Again, our model may lead to a more impressive reality, but ball players are not doing trig. They are almost certainly simulating things, but that does not require trig. Indeed, it only loosely requires math. Models can be very informal with loose approximations.
You seem to think I have to prove your model false to show others don't do that. But I am specifically not claiming your model is false. I'm saying folks don't think that way, necessarily. For example, many build lists for shopping that they were taught. Not that they reasoned.
The ability to build lists requires reasoning. It requires enumeration, inclusion/exclusion conditions, and stop conditions, which necessarily requires logic. This argument is pointless, you go on believing that some people can't use basic logical connectives, I'm sure next you'll say they can't even count.
By that reasoning, though, we can claim that the earth counts to 364 as it orbits the sun. Or that women's bodies count roughly to 9 as they make a baby. These are ways that we model those things, but that is not what is happening.
Most people learn to build lists through mimicry. They literally mimic the lists they were taught they need to build to go to the store. With enough experience, many of us learn to build our own lists from other principals, but it almost all starts with mimicry and simulation. Is why "going shopping" is such a fun game for kids. They are learning.
None of which is to say that you can't make your thinking better with logic. You almost certainly can. But you are begging the question with your examples and explanations. Heavily.
You seem to think I have to prove your model false to show others don't do that. But I am specifically not claiming your model is false. I'm saying folks don't think that way, necessarily. For example, many build lists for shopping that they were taught. Not that they reasoned.