To bind a UDP socket when receiving multicast means to specify an address and port from which to receive data (NOT a local interface, as is the case for TCP acceptor bind). The address specified in this case has a filtering role, i.e. the socket will only receive datagrams sent to that multicast address & port, no matter what groups are subsequently joined by the socket. This explains why when binding to INADDR_ANY (0.0.0.0) I received datagrams sent to my multicast group, whereas when binding to any of the local interfaces I did not receive anything, even though the datagrams were being sent on the network to which that interface corresponded.
Quoting from UNIX® Network Programming Volume 1, Third Edition: The Sockets Networking API by W.R Stevens. 21.10. Sending and Receiving
[...] We want the receiving socket to bind the multicast group and port, say 239.255.1.2 port 8888. (Recall that we could just bind the wildcard IP address and port 8888, but binding the multicast address prevents the socket from receiving any other datagrams that might arrive destined for port 8888.) We then want the receiving socket to join the multicast group. The sending socket will send datagrams to this same multicast address and port, say 239.255.1.2 port 8888.