Neurons are not associated one-on-one with a specific function. There is no such thing as a mirror neuron or the mirror system, just as there is no Jennifer Aniston neuron or neurons for a particular emotion or a particular movement. Just as a swallow in a flock is not a “flock swallow”, a neuron which is involved in seeing somebody else perform one of our actions is not a mirror neuron.
If you cut your finger the pain appears to originate at the site of the wound. But that is misguided. Pain is an emotion that is generated in the brain itself. Pain is always in your head.