Mr Pedantic can say what he likes, as he'd be wrong. In your example, a 275/35/20 sidewall is indeed 96mm. Profile is always related directly to the width, which is why it's used as an aspect calculator. It would be useless otherwise, as who decides what a 'standard' tyre is? Dunlop do a pretty good guide to all tyre marking here.
My rears on the 911 are 305/30, which makes them 91.5mm tall. The fronts are 235/35, which makes them 82.25mm tall.