This paper has a lot of false information in it. The sawtooth wave example is just not correct. There is exactly one band-limited (i.e. no frequencies greater than half the sampling frequency) waveform that corresponds to a set of samples. In the case of a sine wave sampled at twice the frequency, that solution is the exact sine wave that was produced. The video I linked to above has a demonstration of this signal reconstruction, using an analog oscilliscope to show that sine waves are reconstructed perfectly when sampled at only 2x the fundamental frequency.