Sampling theorem clarifications
The sample rate needs to be greater than (not greater than or equal to) twice the maximum frequency of the signal of interest. As @Michael pointed out, sampling a sine wave of exactly 100Hz with a sampling frequency of exactly 200Hz results in data that is indistinguishable from dc.

Reconstructing the input sine wave requires a filter on the output values, not on the input side. (The filter on the input side is for anti-aliasing, another matter entirely.) Ideally, both filters would be brick-wall filters at the Nyquist frequency. See reconstruction filters.