So, you can know precisely which neurons should fire to create a sensation of red (or anything else), and yet not be able to make them fire as a result.

Maybe, but Mary nonetheless by hypothesis knows exactly what it would feel like if those neurons fire, since that's a physical fact about color. Like I said, that's begging the question in the direction of materialism, but assuming that fact is non-physical is begging the question in the direction of non-materialism.