I'm sceptical about DSPS, as my "preferred" pattern is also of 3-4am bed, and 11-12am wake up - but I have no problem adjusting to a normal 12-8ish pattern when I need do.
I think a lot of DSPS is down to how people have their patterns and what's going on rather than due to some medical condition
DSPS is where your body ONLY gets tired at a certain time, out of phase with the social norm, I guess a lot of people who have worked themselves into a pattern by staying up all night and not getting up early for long enough have ended up getting into that pattern, however it wasn't their natural pattern before they worked their way into it, if that makes sense.
I remember few years back at college, I used to go bed at around 4-5am because I coudn't sleep before 4, and be up at 7am, some nights I didn't sleep at all and ended up getting out of bed, this was 5 days a week, then my Saturday was spent with my girlfriend, leaving Sunday to catch up on my sleep (some Sundays I was graced with her presence too, so occasionally I had no rest at all).
To add to things, when I go to the mountains, I'm absolutely nackered, yet I still don't sleep until midnight or later. There's nothing worse than 16 hours on a coach, getting sleep at around 2am, waking at 7am, climbing a mountain and trying in vain to sleep until around 1am... only to be up at around 7am again for another coach journey. Ahh the things I do for fun lol