All strains of flu include a cough from what I understand. He could be sick, but not with COVID-19.
While the visual is not good, there are many reasons for cough. I cough all the time. I have a little tickle in my throat and have a chronic cough. Had it for years annoying as hell, but can't get rid of it. Nothing works. Just saying. On the other had, he may be a petri dish.
I wouldn’t be surprised if it was all a set up by Fox “News” in order to help spread fear.