> If I can feel pain by thinking, what does it mean that pain is "strictly physical"?
It may help to look at it from a cause and effect perspective.
injury -> pain
thinking -> pain
feeling -> pain
thinking -> feeling + pain
pain -> feeling + thinking
...etc
If it means "there is a physical set of physical matter involved in the sensation of pain, be it pain nerves or just me thinking using my physical thinking apparatus", well then given that I'm made out of physical matter, what isn't strictly physical?