[notahacker]

> Most English speakers wouldn't refer to a single person by two distinct proper nouns in a sentence like this, so I'd assume they were referring to two separate people.

I agree with this (though elegant and inelegant variation is a thing). But nor would any English speaker be likely to ask about the skill of an anonymous holder of a position with reference to an ambiguous date range associated with a time in which a later holder of that position would be extensively practicing that skill, which is why I classed it the sort of sentence with no natural meaning you'd only conceive in order to be deliberately ambiguous (or because you don't understand how to write English properly).

The original sentence isn't ideally constructed, but at least the president when JFK was born is a natural and easily identified sentence object, and it would be odd to ignore that in favour of an alternative interpretation that also involved interpreting "how tall" as being more likely to refer to the [probably-not-recorded-for-posterity] length of a newborn infant (who wouldn't be idiomatically referred to as "tall" or the president in the context of his birth) than the height of a person who was president in the relevant time period