If you try to visit a page that doesn't exist on api.stackapps.com, the site doesn't return the "page not found" page; it returns the "we are offline" page. (The screenshots are links to the URLs they show.)
I got the screenshots with Google Chrome, which is set to pre-fetch the page (and show it) every time I change the URL on the browser bar; that is why I was able to show the second screenshot without being redirected.
In the second screenshot I removed the t from "user-top"; I would expect to see the "page not found" error, which is not what happens.
As side effect, if you click on the second screenshot, you are redirect to http://api.stackapps.com/1.1usage; the URL is missing a slash between "1.1" and "usage."