Well, I don't agree that I've misunderstood. Like, there are many subtle levels between me and the professionals in my craft. And there are many, many levels between me and rank amateurs. But the fact remains that Limbaugh probably could sing; if I held hit nuts to the fire, he'd probably be able to croak out at least Twinkle Twinkle Little Star...
It isn't the case that there is a hard distinction between the laity and the priests of music-- we're all just doing our best.
And no, frankly I don't think El Rushbo is up for composing abstract musical compositions; he only thinks he is because he's happily enjoying his ignorance about the reality of music production to score some points in his fantasy of what a culture war looks like.
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But here's a response to the question you ask:
So the question begged by your question: given the importance of context, why does the provenance of a piece of art matter outside of that context?
For instance, s there a difference between the mona lisa "original" and a copy you hang on your wall?
If there is a difference, then the who produced it and the context does matter regardless of who can tell a "fake".
If there is no difference, why would your hypothetical lottery be relavent to the status of art as art... wouldn't the art be in the eye of whoever is trying to judge the work?