[Someone]

“programmable machine are a strict superset of what brains can do”

As others already replied, that’s a statement that isn’t universally accepted to be true.

As an example, there’s consciousness. People disagree about whether it exists, whether it’s (fully) ‘in’ the brain, and on whether computers could in theory be conscious.

There are people who answer those questions with yes, yes, and no, and, since we don’t even have a good idea about what consciousness is, one cannot reliably argue that they are wrong (also not that they are right, of course)