[Phemist]

Unless interrupts and the Input portion of I/O are generated by an oracle (A machine of a computational class more powerful than UTMs) of some sort, a Turing Machine with I/O and interrupts is equivalent to a UTM. I remember the proof being trivial, ie some guys did it during my CS undergrad for a short (2-week) research introduction course, but I can't find a proper paper about it atm. Granted, if the brain was an oracle, this would be true, but you would have to presume that the brain was an oracle in order to prove that it is stronger than a UTM.

In regards to your last statement, the other way works as well. There are statements that can't be proved by any human brain, but can be proved by non-brain logical systems. For example: "The brain cannot consistently assert this statement". One can then create instances of types of problems that are equivalent (when put through some bijective transformation) to the beforementioned statement.