Welcome to QB.
There's also the possibility that this machine was bought used and so the manufacture date wouldn't be relevant. My mother's first machine in the 40's was an old Singer that was converted to an electric machine. So the 1904 date could be accurate even though the your grandmother wasn't that old. Those old Singer's seemed to get passed around a bit. I don't know enough about the vintage stuff but Cathy and Janey know their stuff so I'd go with what they say.