The 'frequencies you can feel' argument is arguable, and probably valid to some degree.
However, there's another argument, which is easier to support with physics and acoustics, to do with the ways in which the response of headphones is measured. Speakers with a 'response' from 20Hz to 20kHz cannot have a nice linear response (same output power for same input level, which is what you want for accurate reproduction of sound) across that range of frequencies, and then immediately drop to no output at all at 19Hz and 20,001Hz. The frequency characteristics of speakers are determined by the frequency characteristics of materials and electronic components, and there's no way to have a steep 'roll off' of this sort, without distorting the frequency response within the wanted range as well.
Any frequency filtering (whether done electrically, digitally, mechanically, or acoustically) will affect a large range of frequencies - theoretically all frequencies (though to a very small degree, far away from the filtered frequency). Likewise, all speakers will probably produce sounds from 1Hz to 100kHz (and beyond) - just not linearly for a given input level.
If a speaker is deemed to have a response from 6Hz to 51kHz, this is probably the range with a reasonably linear response - probably something like +/- 6dB. This will mean the audible range from 20Hz-20kHz can be made lovely and linear, with increasingly poor response between 6Hz-20Hz and 20kHz-51kHz, and worse response still outside that range. If the published range is 20Hz-20kHz, however, you can be pretty sure that at the 20Hz and 20kHz points, the measurement is at the limit of the +/-6dB point, meaning that there will be colouring of the sound, probably from 20Hz-100Hz, and from 15-20kHz, which would be audible to human ears!