As ever, Ted has his own idiosyncratic approach

He's right, of course. Scales and chords are simply combinations of notes. 352? Maybe. But that sounds a little like simple permutations to me rather than musical voicings, of which there must be many more.
I improvised for years using just my ear (well, my hands, too). But jazz is a language. And if you want to 'speak it' you need to know the right notes (or perhaps 'appropriate notes' would be better). Jazz musicians have always been on the lookout for deeper knowledge and different ways of looking at harmony and theory. Bird and Miles studied classical harmony (Stravinsky, Ravel, et al). These days, we're spoilt for choice with good books explaining approaches to jazz improvisation.
For those seeking some kind of method that is not rigid, I recommend Randy Halberstadt's 'Metaphors for the Musician' without hesitation. I'm really surprised I don't see other people raving about his book, too (which is why I mention him when the opportunity arises).
Learning 'which scale goes with which chord' is useful, Bob. But your students should realise that they are one and the same thing. Anyway, all scales and chords offer are a selection of 'notes which work' in a given context. Your ear is the best judge. But when you try different approaches (chord tones and neighbours, scales, licks, etc), you'll give your ear more ideas to work with and use.
Best,
Goose