Read that part more clearly, the important part is "As with". Those firewall rules are regarding setting up udpxy instead of igmpproxy, and the rule they have in common is that they both need to accept IGMP traffic via an INPUT rule, hence the "As with". This program does actually proxy the multicast traffic, since it transforms it into a unicast TCP connection, which means an udp INPUT rule is also required.
From the Wiki:
Above part is actually about igmpproxy and does actually use a FORWARD rule for the udp traffic to the LAN zone as you can also see.
Regarding igmp_snooping, I do have that enabled on my LAN bridge, since without it wireless performance is killed as expected. I enabled it via the igmp_snooping option in my network config file in case that matters.
I'm still extremely confused how my setup won't work with an INPUT rule, but does work with a FORWARD rule. Yet you have the exact opposite.