He's not really applying his knowledge of theory to create his music as he is simply using it to explain and more clearly find the music he always had in him. There are subtle but important differences between the terms "applying" and "using".
I understand your point , although the terms "applying" and "using" are no where strictly defined as one thing or another.
Anthony is not actually "thinking in theory" :
he's hearing the sound he wants to play,
then because of his years of practice and familiarity with the instrument
he is able to execute what he hears in his head.
His ability to almost instantly translate it into scale tones and sing " six five four three two ..."
and know what the name of the pitches involved is
is probably being applied
after the actual playing of the phrase.
I've posted elsewhere that "knowing" an aspect of theory involves 4 components:
- the sound
- how to make the sound on your intsrument
- the name(s) of the sound
- the notation of the sound
With numbers 1 and 2 being most critical.
I guess that's also ideally the order in which we ought to apply it.
Interestingly the order in which we learn is generally the reverse.