For what it is worth I assumed (as I read it) that Nigel was saying the argument was stupid rather than that Chas himself was stupid. There is a difference.
As for the the topic in question Tony Mads already posted a definition. I am not sure of his particular source but Merriam Webster dictionary definitely agrees with him....
mu�si�cian
noun \my�-ˈzi-shən\
: a person who writes, sings, or plays music
Wikipedia states.....
Musicians can specialize in any musical style, and some musicians play in a variety of different styles. Examples of a musician's possible skills include conducting, singing, composing, arranging, and the orchestration of music.
It seems a silly thing to argue about but if we must then the official definitions for the most part seem to concur that a singer is a musician. None of the definitions I could find argue that a singer is not a musician.
Personally it would never occur to me that a singer was not a musician but if that does occur to you then unfortunately you seem to be in an uninformed minority. (that was my nice way of saying that you are wrong

)
Hugz'n'stuff