Yeah, if the OP's concept of "playing through" means barbarically slugging away without utilizing rebound, I can't relate to that mode of operation at all. The terminology is unclear at this point.I can't imagine playing through the ride. I rely on the rebound, it takes about 50% of the work away.
I'd bet you're right about that.I'd start by assuming they both know what they're doing and not recommending bashing thru the ride.
My teacher taught me a ride technique where you have it bouncing of course, but still all fingers making contact, which causes a very woody and clearly defined tick. It drastically changes the sound of the ride, a la Bill Stewart. Maybe that's what he means by "through".
You might be able to generalize that since jazz lives and dies by the ride cymbal, your jazz teacher's advice may come from a place of a higher relationship with the ride.