Yes, I went to that webpage and it says to go to
http://www.usps.org/php/mmsi/home.php, which I did and the page is different from what Nautilus describes. You can't register for an MMSI directly on that webpage. Instead, it's an information page and in order to go deeper into the website, you need to set up an account. The question is whether this webpage is still current for registering MMSI's, as if you go to the new website from this webpage, you come upon this:
Maritime Mobile Service Identity - US Power Squadrons, which appears to be notes on what the new MMSI registration page
would have.