Yes the ISP runs fiber to the DSLAM or the CMTS, and copper is used for the final hop to your home. The latency comes from the buffering and processing required to get a clear signal over copper - for DSL I think you can get in a perfect scenario 7ms or so with fastpath, more if you use interleaving. For fiber you can pretty much treat it as like an Ethernet connection, with latency determined almost solely by distance.