The specific case I'm thinking of was an Advantech AIMB-274 with a Mini-Box PSU (I don't remember which one). I was evaluating this setup for inclusion in a battery powered mobile robot; in particular we needed to decide whether the computer could be hooked up to the battery full time or if there needed to be a relay in between them in order to preserve the battery when the robot was "off". The answer turned out to be that we very much needed to disconnect the computer.

Admittedly this is not a consumer PC or a "modern" gold/bronze-designated power supply, but I still thought it was pretty significant.