ACE-inhibitors are well-known to cause a cough but not like the one you're describing.
If I was to guess I'd say he had a respiratory tract infection that magically disappeared (as they do) not long after ceasing the medication. This is a common type of scenario where lay people get confused about correlation and causation, and is one of the reasons you need doctors to help you.
Even if it was the medication, like I said, this sounds like a somewhat unusual case.
You'll probably spend the rest of your life thinking the doctors didn't know what they were talking about, but in my experience with doctors (I have a lot of that since I'm a doctor myself), even the "median" ones are far better at diagnosing things than lay people.