While you are absolutely correct to ask for a Doctors note, you should know that asthma that is maintained is nothing to worry to much about. Asthma is the acute inflamation of the bronchioles causing increased exhalation effort. Of course it varies in a case by case basis, but for the most part air on land carries the allergens that can trigger a reaction, compressed air is filtered. Air on land has about 80-90% humidity that can trigger a reaction, compressed air is drier, and if they dive Nitrox, there is increased O2 which is used as part of the emergent treatment of an asthma attack. So a lot of the causes of an attack are avoided, and they’re diving with the treatment to begin with.