I've been on a first aid course today (again LOL)
The trainer didn't get onto talking about asthma but i was looking through the book he gave us which does have asthma in and there is NO mention of a cough being an asthma symptom!!!
I mentioned this to him in the break and he said others have said it too
I don't know which 1st aid / medical organisation is behind this cos it's just got our council logo all over it, i would be tempted to email then if i knew!!