Well, that's frustrating.

It would make so much more sense that way, with the blue note coming first, meaning a note that sounds sad or off-color or a departure from the norm, and then the expression "playing the blues" coming to be used as a shorthand way of saying playing the blue notes.

And then maybe being confused with the expression "sing the blues," so that people felt compelled to add sad lyrics to what were originally up-tempo instrumental pieces, and then to change the musical style to sound like moaning and whining.