I see it says "Other error states exist and signify an unexpected internal processing error" under the listing of state IDs, but ... ummm... riddle me this: Why is state 1 is given in the example, as well as being returned in practice, yet is not included in said list? Someone obviously wrote the code which returns state 1. So c'mon, what does it mean guys?
Edit: Found it elsewhere on the 'net. Apparently state 1 means "we aren't going to show you the TRUE state, so we'll try to make your life harder by simply resetting it to another number to get you looking around in circles. The REAL state ID is to be found elsewhere - try your server logs." Yep.. So, the true state id in my particular case is 38 ... *looks at list* Par for the course. Error log says "Login failed for user 'NT AUTHORITY\SYSTEM'. Reason: Failed to open the explicitly specified database. [CLIENT: <local machine>]" Time for more searching via Google for specifics.
Edit again: Thank God for Google. State 38 can also be thrown when, as listed above in the note about authentication modes, your authentication mode is set to Windows Authentication only, and you attempt a named login.