You are right about above, When RP is involved on sending the traffic between source and Receiving Router, It is called Shared-Tree. When RP gets eliminated from the path after source and destination are known together, That is called Shorted-Path tree since that is more efficient path for the source to send traffic directly to Receiving router as opposed to RP being involved along the path and every body has to send traffic to RP even though if it is not a shorted path.
Per my understanding, RPF (Reverse-Path Forwarding) Happens in both situations with RP and without RP. RPF checked depends on the situation. with Shared-Tree, RPF (Reverse-Path Forwarding) happens towards RP (Randeuvz Point). With Shorted-Path Tree which RP (Randeuvz Point) is not involved, Reverse-Path forwarding (RPF) Happens towards source since Shortest-path forwarding is between source and Receiving Router. In Sparse-mode, when we have both (*,G) or Shared-Tree and Shortest-path tree (S,G), always (S,G) Will take over (*,G) which is shared-tree. Due to this matter, when we have both of them, RPF (Reverse-Path Forwarding) will happen towards Source since (S,G) Entry will take over and has precedence over (*,G).
In Sparse Mode, there is threshold=0 with RP by default. Once the first packet is sent from Source to RP, Threshold will go beyond zero. that makes Sparse-mode to switch from Shared-Tree to Shortest-Path Tree which RP will be eliminated and source and Recieving router will start talking directly.
Also, although we are talking about Multicast routing in Sparse-mode, RPF happens in Unicast-Routing table towards source or RP depending on the situations as described above.
I thought to share my thoughts on this