It's official ASUS calculator and it has exact components listed under every category but I'm pretty sure it is way off, for example:
i5 3570k, 4HDD, 4fans, GTX680, DVD-rom gives a minimum of 700W!

Shouldn't that be more like 500 for a single GPU?
Bear in mind that most PSUs are 650.

In a word: yes.

Most PSU calculators are very wrong. The reason is that there is a huge difference in the power delivery of a quality PSU and a mom and pop's "Sure, it'll run 1.81 gigawatts" power supply. So they overcompensate to be safe. The hardware you listed could probably run off a 430w power supply, but ~500 is safe.

My current computer is getting a little old, and has some power hungry components:
Intel Core i7-920 O/C to 4.01GHz (stock 2.66GHz)
ATI Radeon 6950 BIOS flashed to a 6970 (voltage plus timings)
12GB memory
X58 chipset
Dedicated sound card
SSD
Fans
Yada yada yada

The other parts of the computer aren't really important. Suffice it to say it's very overclocked and at full unrealistic load (Prime95+Furmark), my computer draws 470w from the wall. That means the components themselves are drawing around 430w (my power supply is a Seasonic X-460 -- very efficient).

That is very misleading if people pay far more than they need to based on these calculators.

I recommend MSI power supply calculator and Enermax power supply calculator instead.
They are far more realistic than most exaggerating web calculators ......

http://www.msi.com/service/power-supply-calculator/
http://www.enermax.outervision.com/PSUEngine

Rather than looking purely at numbers, look at what conenctors you need also. Like if you're using a graphics card which needs 2x6-pin PCI-E power. A quality power supply maker won't put 2x6-pin PCI-E on a PSU unless they are confident it can reliably push the full 150W combined down them. While you might be able to use a 300W PSU OK for this, they'll take a conservative approach and Seasonic will put 2x6-pin PCI-E connectors only on their 450W models upwards. Likewise they'll be sensible with numbers of SATA and molex connectors based upon power.

So, if a quality PSU has enought connectors to hook up to everything you have, you'll be fine. The TDP calculations will back this up but the manufacturer will already have done this to spec numbers of connectors.

Personally i have always used http://www.extreme.outervision.com/psucalculatorlite.jsp
And found it fairly accurate, I don't tend to trust manufactures calculations.