Seems like he's arguing semantics, to me.
If an instrument is used in the creation of music, it's a musical instrument, and it follows that the person who plays it by hobby or trade is a musician. I don't think the term 'musical', in the context of instruments, is intended to be defined as something strictly melodic... although it can be, in other contexts.
I think your work colleague needs to take a moment to figure out that there are different meanings to words when they're used in different contexts. He's limiting himself to strict literal interpretation, which I'm sure most of us agree is a mistake.
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