Part of this I suspect is that people might already have the symptoms of the side effect but not know it. Almost all of us have random coughs and sniffles and aches and pains, but don't notice them.

Think, for instance, of those times when you've heard a friend or co-worker cough several times over a few minutes and you ask if they are alright, and they have no idea what you are talking about because they were not aware that they had coughed.

When you tell someone the pill they just took might have a side effect of making them cough, they are going to notice those random coughs that they normally ignore, and attribute them to the pill.