The interceptor explodes before the nuke reaches it, throwing a cone of shrapnel in the way of the reentry vehicle. RVs aren't all that tough, actually (they use the same kinda ceramic stuff as is on the space shuttle, and can get damaged by a large raindrop). Also, direct-contact kills aren't that difficult if you have the processing horsepower to direct the missile well enough. Apparently the Navy's Aegis system is fairly good at it using SM2-IVs.
Also, I would point out that a Russian submarine captain (of a Delta IV SSBN) was quoted a few years ago as saying that the targeting packages on his missiles have not changed. It's kinda like a default setting, I suppose, but just because the Cold War ended was not apparently enough to get folks to point their missiles in some other direction.
