> You can have multiple inputs / outputs per bitcoin transaction, so presumably that's what he's talking about.

Actually that's not it. What I'm saying is that you can have any normal multi-party signature scheme, where every N signing-rounds you ensure some measure of canonical ordering by publishing the hash in the bitcoin blockchain. I think sidechains are probably formulated in a similar fashion but it's been a while since I've looked at exactly what they are doing, the trickier parts if I remember correctly are transfers of value on and off the original chain.