I did not mean "random" in a literal mathematical sense. If I have absolutely no idea (or purposefully ignore) what the chord progression of a tune is, I could just start playing notes. It might sound good, it might not. It might sound dissonant in a pleasing way. But that playing would not be based on a theoretical understanding of the chord progression; it would be, in some sense, random -- unplanned, escaping traditional theoretical analysis.

You could play any note on any chord, and it might be what you intended. Let's say the chord is C major. You could play a C, for the root. Or G, for the 5th. Or Db, for a flat 9. Or F#, for a sharp 11. Indeed, any of the 12 notes would be fair game, and you could name what they are from a music theory standpoint.

Trying to bring this back around to the Franklin method of learning: what one might do here is listen to a jazz solo, and first transcribe (or obtain a copy of) the chord progression. Instead of trying to copy the solo itself, you can hear that the soloist often played motifs emphasizing the dominant 9th and 11th over minor chords, and the major 7th and major 6th over major chords. You could then make up your own solo with the same emphasis. It would not be the exact same solo, but it would (or could) have a similar sonic color to it.