Haemus, here are the files as downloaded from the site you mentioned, for 16, 8 and 22 kHz:

Basically your computer/iPod whatever will have to produce a clean clear sine wave of 8, 16 and 22 kHz, starting with the samples marked by the dots. It needs a good, precise, low noise DAC and an exceptionally good analog filter after the DAC as to produce sine waves from the crap you see.
My bet is that no one would hear 22kHz for the simple fact that most brick-wall filters in DACs these days are tuned lower, at 20.5 - 21 kHz.
OTOH yes your son hears some signals that you don't, but are you sure what those signals are?
Short of checking with a good mic and an oscilloscope, you cannot tell what the earbuds are producing when the phone plays those files.
Nap.