How does material identity theory of mind deal with private subjective experiences?

I'm currently reading a book on the philosophy of mind, and so far it has been fantastic but one part didn't make any sense when the author attempted to explain it, about the materialist identity theory of mind.

Basically, let's assume you are in a neuroscientist's office. You look at a red apple. The neuroscientist opens up your head and peers into your skull at your brain to see what is happening and identifies the specific area of the brain that seems to be responsible for the experience of a red apple.

However, the neuroscientist does not actually see the red apple, he just sees the neural synapses occurring.

The trouble with material identity theory then is that if we are to say that mental properties are identical with physical properties, then what the neuroscientist himself is experiencing is an experience of an experience of a red apple. So like experience-ception. Which is obviously not happening. The neuroscientist obvious does not intrude on the private experience of the patient.

Now, I find it hard to believe that materialists would not have thought about something like this, and the author of the book describes one way around it by appealing to something called the "phenomenological fallacy" and something about having an experience being equivalent to observing an experience.

So I'm looking for some clarification on this. Thanks.