Here is the mindset I would go with:
A "working interview" should be a time where the hiring doctor is evaluating the new doctor on their patient care, bedside manner with patients and interactions with the staff.
The doctor that is getting interviewed should use this time to evaluate the flow of the practice, the level of care provided and whether or not they want to call this new place home or not.
For a hiring doctor to ask for a "working interview" it means that the hiring doctor thinks enough of the new doctor to spend extra time with them to evaluate whether they are "the one" to invest their time, money and energy into. Therefore, both the interviewer and the interviewee are receiving benefits from this time spent together.
If lunch is provided and there is a chance to get to know each other better on more of a personal level, that is a bonus. I would not be concerned about getting paid for that time as it is time well spent and you should be flattered that they chose you over all the other applicants to further evaluate you for the position.