There is absolutely no evidence that animals or humans function as just statistical machines of any complexity.

It's a fallacy to think that way. You can find statistics and probabilities in human actions, yes, but that doesn't mean that's how they are formed. Ask enough people to guess the number of beans in a jar, take the average and you'll be pretty close to the actual number of beans in a jar.

But that doesn't mean that any one human, or humans in general, are intelligent or not intelligent. The intelligent animal would open the jar and count them. Even the humans that are guessing are not basing their guesses on statistics or their experiences or their genetics. They are formulating a reasonable method to calculate the necessary number to solve a very, very, very narrowly-specified problem.

That's not where intelligence is visible or thrives.

Anything sufficiently complex system, even physical, mechanical, unintelligent, rule-based, etc. will confirm to similar probabilistic properties. That doesn't prove the creature isn't intelligent, nor that the intelligent creatures are based on those statistics.

In fact, it also falls somewhat into the gambler's fallacy - overall enough data points will conform to average out the reds and the blacks almost perfectly. But you can't rely on that average, or your knowledge of statistics, to predict the next colour the ball will land on. That's not how it works.