It should... but again, other factors can come in to the mix, that make it not quite 100% that simple.
The poster maker is generally the party with the least power in any case, and who will end up getting it up the pooper regardless of who is right in a dispute between promoter/band or promoter/artist.
Working poster artists have to maintain lines of communication with promoters as well as bands. It's down to the individual whether it's a good call to burn that bridge or not, regardless of who has what rights.
Not saying that's how it should be, just that's how it often plays out.