I glossed over the SCYSA complaints and you pretty much understood it, dhunter. The main complaints were that SCYSA insurance does not apply to any non-affiliated organization, that a fee of $50 must be paid by any non-affiliate intending to participate in a "sanctioned" SCYSA tournament, and that SCYSA teams are "sanctioned" or allowed to play in unrestricted or unaffiliated tournaments or to travel to play non-affiliated clubs.
Basically, it looks like SCYSA enacted a bunch of rules to try to keep their players in SCYSA and away from joining additional teams or switching organizations. Instead of being allowed to play teams from any organization and playing in any tournament, everything is funneled exclusively towards SCYSA/USYSA related events.
It seems that AYSO, US Club Soccer, and the other named organizations want there to be a relaxed flow of play amongst the varied units so that a Club Soccer team can play in USYSA tournaments or against teams outside of their own sanctioned Club league seasons without their incurring some sort of obscure fiscal penalty.