1. RFC 7761: Protocol Independent Multicast - Sparse Mode (PIM-SM), Section 4.5.1, "Sending PIM Assert Messages". The document states: "A PIM router sends an Assert message on a multi-access, multi-PIM-neighbor LAN when it receives a multicast data packet from a source S on an outgoing interface for an (S,G) entry." (DOI: https://doi.org/10.17487/RFC7761)
2. Nokia 7750 SR OS Multicast Routing Protocols Guide, Release 21.10.R1, Section: "PIM Assert". The guide explains: "The PIM assert mechanism is used to resolve the issue of receiving duplicate multicast packets. This can occur when more than one router is forwarding multicast traffic onto the same multi-access network." This confirms the scenario where a packet is received on an OIF.
3. Kurose, J. F., & Ross, K. W. (2017). Computer Networking: A Top-Down Approach (7th ed.). In Chapter 4, Section 4.8 on Multicasting, the PIM Assert mechanism is described as being initiated when a router detects that another router on the same broadcast LAN is forwarding the same multicast datagram, which it detects by receiving that datagram on its own outgoing interface.