If the practice fights this correctly, I'd say the person would have a really poor chance of getting his unemployment benefits approved, regardless of what state you are in, though we'd sort of like to know.
In the first place, I would strongly encourage you to read very carefully the material your office receives from unemployment insurance. Secondly, I would strongly advise you or the doctor or the person who will be handling this (I suggest the practice manager, if you have one, or the one who does the doctor's paperwork, writes the letters) say that this person was fired for misconduct and insubordination. That he was asked to do paperwork to collect some statistics about the success rate of the programs he was working on and doing for the office, and he refused, saying he wasn't hired to do paperwork. Then he was insubordinate to the doctor who was his supervisor, and was refusing to do what he had been asked to do. His information about how much he has helped the practice is not correct, and when he was questioned and asked to show proof of how effective his work had been, he refused to cooperate and showed real bad attitude and disrespect for his employer, and was asked to leave for that reason.
DO NOT say he was fired for poor performance. Poor performance is almost impossible to document, and he will probably be approved if you use a performance issue. All he will have to say is that he did his best. Use the ugly scene when he was told to leave and call it gross misconduct. Say that he was insubordinate, that he refused to do what his employer asked him, argued, and was loud and belligerant. This was much more serious than whether his job performance was good or bad.
If your employer asks you to do something, and you refuse, that's pretty generally misconduct, unless you are asked to do something illegal or immoral. A request for him to give you feedback and actual documentation about the effectiveness of the program he was working on was certainly not an unreasonable request. And I gather from your posting that you and perhaps other staff were witness to this confrontation.
Be sure that you send back the inquiry letters or return the telephone calls in a timely manner. It would be better for you to use good documentation, not just have the doctor call them and tell them he/she doesn't want this person to get unemployment.
I cannot tell you how many times I was contacted by doctors, most of whom had no clue what they were talking about, trying to give me orders not to approve a person's unemployment claim. Sometimes it worked, sometimes it didn't, always based on the actual situation. Actually, this case to deny is pretty good, but use good judgement, answer all the agency's questions carefully, do everything in a timely manner.
