As I understand it what Quick says to do (assuming whoever quoted him understood him correctly, which is not certain) is not to arch your back, but slightly tilt your head forward and then fix the resulting balance problem, by pushing your upper back into the water. This shouldn't increase the arch of the back.
Still, this is different then what I try to do in the pool. I try to keep my hips and belly at the surface, but I never try to tilt my head. I always aim to look straight up with only my face above water.