Simple counterexample to sampling theorem

Question

I know this has to be wrong, but can't see what is wrong with it:

Take a simple sinusoid. It crosses zero every half cycle. Sample it at double its frequency. If the samples coincide with the zero-crossings, you get all samples at zero. In that case, you cannot know the sinusoid's amplitude from the samples.

Anybody could spot where my mistake is?

Answer 1

The answer is stated in the article: "Modern statements of the theorem are sometimes careful, explicitly stating that $x(t)$ must contain no sinusoidal component at exactly frequency $B$, or that $B$ must be strictly less than half the sample rate."