It works because of how hard drives work - the heads are extended by slightly heating the bar the heads are connected to. If you're head crashing, you need a little less length, hence freezer.
This isn't quite true, the heads are kept from crashing by air pressure and a crash does irreversible damage. The "clicking" sound is either the heads flicking back and forth as the drive tries to seek, or the central motor trying and failing to start platters spinning which are jammed on the bearing.
What freezing the drive may achieve is either un-sticking it from the bearings (see also the "bang drive on edge" technique), or lowering the thermal noise floor in the electronics enough for marginal components to make it through the boot sequence.
When I worked for a small computer place years and years ago we'd sometimes "tap" a drive as it was spinning up if freezing it didn't work. Tapping it with a screw driver handle rarely worked, but it was always a last ditch effort to save having to send a drive out -- which most people wouldn't pay for anyway.
I did that with a drive in my computer fairly recently. Although I didn't so much tap it as shake it on startup. It did finally start spinning enough to insure that I had the last few bits of data transferred to a new drive, though. :)
While they may make legitimate points in the article, it's hard to consider someone that makes money on HDD recovery like the authors of the article having an unbiased viewpoint here.
