Maybe. It also could be that the frequency range is defined by different criteria in each case. In the case of the amp it could mean that the amplitude stays within +-0.1dB , or even tighter, in the whole reported frequency range.
In headphones it can mean whatever the manufacturer wants it to mean. Could be that in most companies the marketing departments makes them up. If you take a look at the frequency response charts at InnerFidelity, you'll see that they wont stay within tightly defined boundaries. There can be peaks and valleys 20dB or more apart. If you applied a +-0.1dB critera, many headphones, even good headphones, would have a frequency range of something like 80-300Hz, or less.
And, anyway, you won't hear that 20kHz-30kHz range, and there might not be much stuff to hear in those frequencies even in "hi-res" recordings, even for your dog, so there is not much point in worrying about it.