It's not ridiculous, and the 'know it when you see it' stuff is only because people used to struggle to articulate it. But it's obvious. The elite QBs can and will successfully improvise on a regular basis, either with their arm or their legs. Hurts obviously does the second very, very well.
I'll say this for Purdy, maybe he can or would be a gunslinging, improvisational wizard, but it's clear that Shanahan wants nothing to do with that kind of QB. He wants a pocket-passing statue that will run the play and the prescribed audibles as called.
It's possible that if Purdy had Andy Reid or Sean McDermott as a HC, he would have the freedom to take the reigns and steer the ship his way when he sees fit, but he doesn't so it's hard to say he's an elite QB.