[icegreentea]

Ah ok, so here I think is the slight confusion.

If you make the constraint/assumption that during reconstruction that you rebuilding a time domain signal composed of series of sinusoidals, then you're in the clear at just 2x sampling. For example, in Figure 2 in the article, it states that 2x sampling only provides frequency information, and not amplitude and shape. This is true if we assume that we're trying to directly reconstruct -any- periodic signal. Then if we sample at only 2x of the signals fundemental frequency, we are in fact stuck.

This can cause certainly cause confusion. So I think the usual way (I just dinker with DSP for funsies and a little bit at work, so I might have got it mangled) to deal with this confusion is to remember that sawtooth and square (and whatever) signals are chocked full of high harmonics that also must be sampled at or beyond the nyquist limit for you to be able to construct it.