I like that analogy, even though I'm not sure I agree with it.
The fact of the matter is that under current storm naming protocols/rules, if a named storm travels from one body of water, across land, and then into another body of water, the storm is renamed. It doesn't matter if the storm maintains itself or not, so in this instance, the origins of Arthur are irrelevant in its naming. Now, whether that protocol makes sense, is a matter for debate, but I think it does, because let's just say that this system had been kept as Alma, and then somehow moved into the central Gulf, grown stronger, and made landfall along the U.S. coastline. Then, the "first" storm to form in the Atlantic basin is given the name "Arthur"... which would cause significant confusion among the public. So, the "right" thing to do is to name this "Arthur" from that standpoint.

The flaw by the NHC is to state that the reason the system was named Arhur had anything do to with Alma other than the fact that it crossed from one body of water into another and was renamed by established protocol.