Even though you can flight instruct using the privileges of a third class medical cert
The way I read the rules you can NOT for compensation or hire---as in he instructs for free.
Also, EVERY company I work for has kept a medical on file for all pilots. I have a "status" board on the wall in my office showing the expiration date of all my pilots medicals, 135 rides due, carding rides due etc.
I cannot even comprehend why a professional pilot would let their medical privileges expire...except for medical reasons...