I would've also expected the DC-DC converter to have a wider input voltage range than that: 10V to 15V at least, otherwise it's pretty pointless.
5% could be a mistake, I'd send them an email, asking for clarification.
Perhaps the 12V output is directly connected to the 12V input?
Looking at the board, there are only three large energy storage inductors, probably one for +5V, 3.3V and -12V so I suspect that's what's going on, unless the little one on the right is for -12V, although I suspect it's just an EMI filter.
Try disconnecting the power from it, waiting a couple or minutes or so for the capacitors to discharge and measuring the continuity between the 12V output and the 12V input using a DVM, if the resistance is very low, (<0.1 Ohm) then you have the answer: there's no 12V DC-DC converter so the 12V input has to be within the range specified by the computer.
If this is true, the DC-DC converter isn't much use as few 12V supplies will be that well regulated and I imagine that the main use for such a supply would be to run a PC from a car battery which it can't do. If so, see if they except returns and look for a better PSU, otherwise look for a 10V to 15V to 12V 5A DC-DC converter.