Nonsense, you can run DC power to an AC device that uses a line voltage bridge rectifier, provided the DC level is the same as the RMS AC level. What do you think a bridge rectifier does? Converts AC to DC. What happens when you pass DC through a bridge rectifier? You get DC, just with a 2 diode drop after. End result is still DC.
The only issues you might run into are polarity and damaging contacts from arcing when plugging in, the UMC does a ground fault test, and it might not like it if the ground or negative input of your DC is not on the same terminal where the neutral normally would be. When plugging into DC, you need to be sure its a true DC outlet, to avoid arcing and damaging the contacts. You would probably need to make a dongle or pigtail adapter for the UMC, so you can use a proper DC connector, or have an on/off switch for the outlet so it is denergized when you plug in.