I agree with the "Who knows..." crew. While the military has specifications for everything, they are also excellent scroungers. You could easily put together a story of a motorpool finding and conscripting an old Model A into general utility work around a base in the US, a unit hack. Probably less likely in Europe or the Pacific. You should consider adding some unit markings to the bumper, something like 6C 28R * HQ3 (Third vehicle, Headquarters unit, 28th Recon, 6th Cavalry) to add to the story.
Local veterans groups, re-enactors, etc. will love it. You'll also be the hit of the Custom Cruisers car show when you show up.