(Lots of math at those links - but Wikipedia is pretty decent at this sort of thing where you can copy the formulae straight out of any electrical engineering text book.)
Most signal processing systems we have (especially PC-based ones) are designed to sample at rates that work well with sounds that are generally well within hearing range (CDs sample at around 44KHz - so can only cope with a peak frequency of around 22KHz - and mobile phones sample at much lower frequencies to save bandwidth and use complex coding schemes to fake the dynamic range). Apply one of the common audio-processing packages to a near ultrasound, and you're going to get harmonics in the resulting sampled sounds.
Without knowing how the sound was sampled (or created), and whether it was passed through any anti-aliasing filters there's no way of knowing just how pure the tone is. There's certainly no way we can trust the test people have been doing: its tones are mp3s that have been put through the Flash codecs, they've been sampled and desampled several times, so aliasing errors will have compounded.
Sorry folks, but it's all, err, bollocks.
If you're worried about your hearing go see your doctor.