The thing is, if the sample rate matters with respect to anything other than the Nyquist limit, your filtering isn't good enough.

Relying on spacing between sample clock harmonics to keep beatnotes out of the passband isn't great engineering practice. I have to do that in a relatively-exotic RF application, admittedly, but I wouldn't advertise it as a feature. :) And I'd never choose that approach at audio frequencies. There's just no need.