Do you have trouble with 3D printer on UPS during short power outages?
Part of your self-answer:


  What is puzzling is why did the 3D printer run as if the computer was still operating it, when is was printing from the SD card? Was the circuitry getting power from the USB cable from the computer?


is more of an extension of the question, which I'll answer. Generally, yes, the logic of many (most?) 3D printers can be powered by the USB connection. You can try it sometime with the printer not plugged in to the AC power source at all. Under such a power configuration, the motors (not to mention the heating elements) should not operate at all, and I think the firmware has logic to detect this condition and not try to print under it, but I may be mistaken. However, in any case, in the event of an outage during printing, the logic board will remain powered if it's connected by USB, and especially if the outage is short enough, it might not even notice that the motors and heating elements are not functioning, yielding a result like what you saw.