In a speaker chain (like a floor standing home setup), the volume control is in the preamp and not in the amp. So you're already controlling the volume immediately at the preamp input (much like controlling it on the DAC)
Same situation in a headphone amp. The volume control is in the input.
The problem is in the nature of a source vs. other components in an audio string. With a truly weak signal source, such as a microphone, phono input, or tuner antenna connection, the last thing you want to do is attenuate an already very weak signal. That's because you're often at the physical limits of reasonable gain ratios, and noise, hiss, and hum will be the result. The alternative is to attenuate the signal on the output (for a source). That function is already provided in most audio strings by the pre-amp or headphone amplifier inputs.
In the case of a DAC, of course, the signal on the input side is undergoing a conversion from a digital form to an analog form. You don't need to read the datasheets to figure out whether a DAC (or software music player) is affecting the quality of the signal stream if it implements volume control on the input side: it can't be done any other way. Applying an analog attenuation to a digital signal stream is impossible. Thus, the digital stream is manipulated if the volume control is not on the output. You can argue whether that affects the quality, but the very idea is in conflict with trying to preserve the digital stream as "untouched," which is the goal for which every audiophile strives.
If an analog attenuation is placed at the output of a signal source ahead of a pre-amp, or if it's placed in the preamp - it makes no difference. The function is the same in either component, so long as it's not included in both. If included in both, then you get the ubiquitous question that keeps getting asked on Head-Fi - "How do I best control volume, with my DAC or my amplifier?" You also get twice the noise, because you have two attenuation circuits that the analog music signal has to traverse. (If there weren't noise consequences to using analog volume controls, there would be no market for expensive stepped attenuators.) There are RC circuit implications as well (potential bass loss), depending on whether output or input capacitors are present.
P.S. A Jedi said it much more simply.
