That doesn't sound anything like your typical low-pitched head-positioning sounds. I doubt the voice coil positioner is capable of vibrating that quickly to produce those high pitched tones. Given a seek time a few milliseconds, the most they could hope to produce would be a few hundred Hz. Those tones sounded like a couple KHz.
Also, there's a definite pure, harmonious quality to it. To my poorly trained ear, it sounds like a pure sine wave. Musically, it sounds like a perfect fifth followed by a major third interval. Head movements and their associated vibrations sound more like noise due to all the random interactions. I still think it sounds like a small speaker inside, probably a little piezo tweeter.
BTW, there is air in the hard drive. In fact, that air is critical to a HDD head's ability to glide just microns above the platter. Also critical is the spinning of the drive. The spinning helps form the air cushion. Without the platters in motion, the head "crashes" and gets stuck on the platter... which precludes the positioner from moving at all. Scott said that the hard drive doesn't even spin up.
I agree that the freezer trick should only be used as a last resort. But bearing life isn't a big issue since the hard drive is most likely going to be either discarded or returned for replacement after recoving the data. Actually the last resort would be to send it to a data recovery shop, which charge a hefty amount for their services.
BTW, I forgot to add that it's a good idea to put the HDD in a bag, suck out as much air as you can, then stick it in the freezer/fridge. This will keep too much moisture from condensing on the HDD.