They can always ask but you don’t have to provide for sick. Part of the problem can become when pilots just start sending doc notes for the flu. Over time practice has the potential to become statue quo.
There is a difference legally when coming back from a medical leave of absence. Part of the reason that language is in separate sec of an agreement.

I was asked at one point for a doc note from the chief pilot to provide a doc note for a sick call. I responded to the email and said I never went to the doc. He responded back with ok thanks. I made sure I got paid for it then sent the correspondence to the union for archival.
Next time the plan if it happens will be my wife didn’t go to the doc to solidify that part of sick language.