This article says that the PIM designated router is separate from the "PIM forwarder" (router which forwards multicast traffic to the multicast receiver on the LAN).
Why aren't the PIM designated router and the "PIM forwarder" always the same? The PIM designated router is responsible for sending PIM joins to the RP. That should always be the same router that forwards multicast traffic to the host wanting multicast traffic for that group.