ITA's site actually predates Hipmunk and the Google merger.
The reason ITA keeps it a secret is because ITA is a middleware company and not consumer facing. Bing, Hipmunk, Kayak, Orbitz, Hotwire, and many more are all customers of ITA[1] and it takes pains to not compete with its customers.
That's also why everyone was freaking out when Google offered to buy ITA. Google could have easily pulled the plug on all of those sites and taken over the industry. So Google had to commit to tons of concessions to ensure that wouldn't happen in order to get approval for the merger. Basically, Google has agreed to ongoing audits by the Justice Department for years after the merger. [2]
For a long time matrix.itasoftware.com was password protected but bugmenot/bugmenot worked. I am not sure when they made the search service non-password protected. I imagine if it gets popular, it will go back to being password protected, as it is rude to compete with your own customers.
The older version of matrix - currently available at http://matrix1.itasoftware.com - had a not-so-inviting page asking you for a login if you had one, but never required it. There's a "Log in as a guest" link that gets you to the same page you'd have as if you had registered as a typical user.
They aren't competing with their customers - you cannot book a flight on the site. You have to take the booking information ITA provides and call the airline yourself.
The reason ITA keeps it a secret is because ITA is a middleware company and not consumer facing. Bing, Hipmunk, Kayak, Orbitz, Hotwire, and many more are all customers of ITA[1] and it takes pains to not compete with its customers.
That's also why everyone was freaking out when Google offered to buy ITA. Google could have easily pulled the plug on all of those sites and taken over the industry. So Google had to commit to tons of concessions to ensure that wouldn't happen in order to get approval for the merger. Basically, Google has agreed to ongoing audits by the Justice Department for years after the merger. [2]
[1] http://www.itasoftware.com/about/customers.html
[2] http://www.nytimes.com/2011/04/09/technology/09google.html