This is a common misconception.
Ok, so here's the thing. If you look at the digital samples, that is true. There ends up being like 2 samples per period or something and it just "looks" like a triangle. The part you're forgetting is D/A converters. You're not hearing those discrete samples. What you end up hearing is reconstructed from those samples, and is a perfect (well, depending on the D/A converter quality) reconstruction of that sine wave. This just follows from the Nyquist theorem.
The digital sampling is obviously not perfect, but you're not hearing the digital sampling. The discrete samples are just a representation of the bandlimited (lowpassed) analog signal, and those discrete samples are sufficient to perfectly recreate that analog signal.
Another way of thinking about it: there is a finite amount of data in a finite-length bandlimited signal! Bandlimited is the key word here. If there is an upper limit on the frequencies that are present in an analog signal, then we can discretely sample that signal in such a way that no information is lost. The discrete sampling is not an approximation of the signal -- it is a representation of the analog signal that contains all the information present in it!