Of course it's not getting all that power - not only would the driver melt, so would my ear drums. But I have to politely disagree with the "no matter what amp - they give the headphone the same amount of energy." This might be theoretically true if the impedance of a headphone were constant and fixed, like a dummy load, and if music was fixed a specific frequency. But no headphone is made like this. Some can vary dramatically over their range. And a music track's dynamic passages can vary significantly as well.
The HD650's impedance is rated at 300 ohms, but it actually varies over its audible frequency range - hitting 500 ohms at about 100 hz (almost 2x the rated impedance). Other headphones can vary up to 10x the nominal impedance.
At louder levels and with music that presents high dynamic range, both hypothetical amps would need to deliver a sufficiently equal amount of voltage across all frequencies to match the same levels of loudness. And of course, they don't unless the amps are identical. As Woo's comparison page shows, the WA22 delivers much less power as headphone impedance varies (700mw at 600 0hms vs 1100 mw at 300 ohms) in comparison to the WA5, which drops from 6000mw to 4000mw (which is a much lower power drop as the impedance rises - a testament to both its beefier transformers as well as its more massive caps).
Two differently rated amplifiers powering the same headphone at the same loudness level over the course of a song will not deliver power in the same fashion - the lesser amplifier will tend to clip or distort earlier, and it may not effectively have enough voltage to control the driver in the critical low frequencies and lower mids. The listener hears this deficiency as sloppier bass and flattened soundstage. You don't need a high powered amp like the WA5 to experience this - just listen to the HD6xx on an iPOD, and then on suitable desktop amp.
This is more often the case with loudspeakers (a speaker like the Apogee Duetta presents a 1 ohm load in its lowest frequency - lower powered amps without sufficient power reserves can actually perceive this as a short as they try to double power output as impedance drops - and then shut down when their capacity is exhausted).
I'm over simplifying this, but my main point with the HD6xx is that welcomes the extra power of an amp and produces a tighter, more defined low end and much better mids/highs and a deeper soundstage with the more powerful amp - and at louder volumes especially.
