I think what Kazan is saying is that the Method isn't a thing. It's an action, a process, a skillful or effective way of achieving a specific artistic task. It's not a pair of shoes. It's discovering how to walk. I did an affective memory at the Actors Studio years ago, after which Lee Strasberg said, "Now that's an affective memory. Darling, tell them how you did it." When I explained my process, Strasberg replied, "That's not how you do an affective memory! But that's what the Method is all about. It's a way of work!" You find your own way of carrying out your own and your character's internal truth—within your body, mind, and soul.
As quoted in "The Method and the Myth" by Robert Walden, in Backstage (April 21, 2009)