Minimum connection times presume that the passenger is familiar with the layout of the station, and that there are no broken down lifts or escalators.
12 minutes at Birmingham New Street would be challenging for me, and I am now reasonably familiar with the station (although I couldn't find the Virgin Lounge last week, even though I've been there before!), so if someone who doesn't travel frequently, or has not used that station before, tried to make a connection from one end of it to the other in 12 minutes, given the usual crowded environment, they would have to have all their wits about them. And that's just the able bodied!
(Edit: I know we are not discussing BHM, my comments are for illustration of the general principle.)