Without knowing excactly what Pinback uses for their sounds we're kind of shooting in the dark. I listened to the 2 tunes off their site, and agree that the drum sounds are pretty good. Sounds more like loops than a machine.
The most important thing about canned drums is to start with sounds that are real close to what you want. It's been my experience that drum samples, especially the ones in most drum machines, don't respond well to heavy effects. Then again, that's also true for real drums.
One thing I noticed about the Pinback stuff was that the cymbals are not very prominant in the mix. That's usually one of the weak points of sampled drums. They also seem to be using a good room verb on 'em which adds to the realistic sound. I bit of ultra-high roll-off, and a good room verb can work wonders for taking the gristle, and dryness out of canned drums.
The actual programming has a lot to do with it as well. If you can think like a drummer, and program your parts accordingly it will help. I've found myself running out of memory when programming drum machines because I use lots of different parts with subtle variations to get a more "human" feel. This is where loops shine. The feel is already there so as long as you mix the parts up a bit it works well.
My golden rule on 'verb is simple though: if you notice the 'verb right away it's too much.