It is a little hard for me to interpret their comment. I took it as meaning that the learning strategies should differ for pure and applied mathematics, hence my response.
Maybe another way to say this is: pure math is just a kind of applied math where the applications are resolving theoretical problems. Essentially all of the big mathematical programs/fields/whatever were created to solve or understand some Big Central Theoretical Problem(s), and prove their worth by continuing to be useful in solving other problems. And generally these problems can be understood in terms of concrete examples.
Even Grothendieck, perhaps the canonical example of a "theory builder," had resolving the Weil conjectures firmly in mind while writing his famous texts (and then got annoyed at Deligne for doing it the "wrong way"; see https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircl...).
