Well my last theory of a Spanish marque proved incorrect, but I now know it is, in fact, a US marque, and that, along with the additional photograph, helps.
The statement that the car "is from a relatively well known maker" leads me to believe that, although the marque isn't obscure, it also isn't from the really big names. The thing that keeps bugging me is that the puzzle car has wire wheels. It must be a pre-1921 model, when the assassination occurred, but at that time the majority of US marques used wooden artillery wheels. Also, I find it rather incredible that news reports of the day all refer to the car as a Hudson, when it isn't.
I still think that the President would be riding in a prestige marque, so the question is: What US prestige marque, from the correct time frame, has wire wheels and a name that might be confused, by a harried non-English speaking reporter, with Hudson? The result of this line of thought is a: Jordan from about 1919.