This is funny one. It took me a while, but enjoyed it.
The source for that site contains:
<div>
<!-- Please DO NOT use this site to power an IP bot, script or other IP-lookup software! -->
<h1>Your IP Address is <span id="ip">a random ip</span></h1>
</div>
It is kind of anti bot mechanism (they even warn about it :D ). On page load it's replaced by your actual IP using Java Script.
I checked other sites and most of them use similar mechanism.
This one does not if you need to check http://whatsmyip.net/