I am not confusing the two. In a band-limited signal, the Shannon-Nyquist theorem mathematically proves that the sampling rate is the frequency resolution. It also proves that when a signal is band limited, discrete time sampling can be a zero-loss transformation.

Your analogy misunderstands audio signals. The resolution components of bit depth and lossy compression are different axes and should not be conflated with or analogised to frequency resolution. They behave very differently.