That sign looks to be put up by “Bethesda Urban Partnership, Inc.”. Hardly the cognizant goverment authority, so I don’t think that’s a relevant counter-example.
I think this is fine because both are in use and there’s a clear distinction between Washington the city and DC the federal district. I am more interested in the general rule that we’re applying to make sure it works as well as possible in all places we’re applying it.