There is an interview with Maureen Tucker at moderndrummer.com. Apparently they did a two-part series on playing drums for the Velvet Underground. Here's a bit:
Let’s talk about a couple specific songs. On your Web site, you describe “I’m Waiting For The Man,” and how everybody played so heavily on all four beats.
I love that song. It’s like a train, there’s no stopping it. When we were rehearsing for the ’93 tour, we weren’t three or four bars into it and everybody stopped, like, what the hell’s the matter? I knew what the problem was, but I didn’t say anything at first. But eventually I was like, “Lou, you have to play all down strokes.” He had forgotten that. Just the difference between playing down-up-down-up and playing down-down-down-down was incredible.
This is a good example of how being in a band hampers Advancement. Perhaps there was some new magic to be made with down-up-down-up. But because the band wanted it down-down-down-down, that's the way it went.