Considering I have had a cold for almost a week and severe cough since Friday from over exerting myself at the gym (30 minute RPM class where I flogged myself...dumb in retrospect) this is alarming.
So Froome was coughing at the end of the stage and he beat all those guys? Yeah, I know how that plays out in the normal world. It hits you hard. Really hard. I've had it happen before. It's enough to completely destroy your ability to breath at higher aerobic outputs, because the oxygen demand on your lungs is so high. That ain't normal. You wouldn't be able to exercise properly at all, much less ride a Grand Tour and beat everyone.
To do so would require some uber powerful drugs, lots of rest, no exertion and more drugs. Another thing to sell this Sky fable as totally *legit*.
The manner and type of cough does differ, but basically, from experience, if you get a bad cough, even a mild one, cycling is about the WORST idea one can do. You exert yourself, you make it worse. Body needs to heal. Needs TIME to fix itself. Oh but doing things naturally isn't the Sky way is it!