Why do I need more samples per cycle then the Nyquist theory would lead me to believe?

Why do I need more samples per cycle then the Nyquist theory would lead me to believe?

In practical situations, Tektronix oscilloscopes need a minimum of 2.5 samples per cycle. If the samples always happened at the peak, then the oscilloscope could work all the way down to Nyquist.  However, when you are at Nyquist (2 samples per cycle), the amplitude is infinitely variable because the timing of the scope's samples and the signal are asynchronous, meaning that the 2 samples per cycle are sometimes at the peak, sometimes at the zero crossing, but mostly it's somewhere in-between.

Below is the real world in the form of screenshots.  Note just how well things are working at as little as 2.5 samples per cycle, however there is a roughly 5% error in the peak to peak amplitude measure going from 10 samples per cycle down to 2.5 samples per cycle.  So despite the fact that the SinX / X interpolation that works very well, more samples are still better.

Figure 1: 2 samples per cycle 2.5 MS/s with 1.25MHz sine input at 2 V p-p

Figure 2: 2.5 samples per cycle 2.5 MS/s with 1.0 MHz sine input at 2 V p-p

10 samples per cycle is a good minimum rule to get the best accuracy for a signal:

Figure 3: 10 samples per cycle 2.5 MS/s with 250KHz sine input at 2 V p-p