I like both of the examples of ringing snare sounds that were posted, and I believe the Vinnie clip is a great illustration of the evolution of drum sounds in recordings. Some of his older works used that muffled 70's type sound, and gradually we've seen this change to a more open sound.
I could be way off base, but having listen to music as it happened for over four decades now, I always felt the changing drum sounds largely reflected the techology of the day. The70's (maybe even earlier) brought close micing, but the drums needed to be muffled to capture a pleasing sound. As microphone and recording technology improved, the ability to capture a more natural sound emerged.
I don't know if that is truly the case, but that's how I thought about it as I was listening to it happen. I always felt that the preference for a muffled snare was a byproduct of being used to the sound produced by the technical limitations of the day.