Let me start by seeing if I'm guessing on the right track.
It seems to me that the ONLY way you could scale to this degree is with a segragated witness style scheme. VERY VERY roughly it seems like the idea would have to be that each node will only monitor a small fraction of the total network, and any time you are interested in a transaction that is not taking place on the part you are monitoring, you will be forced to trust the consensus of the percentage of the network that IS monitoring the transaction you are interested in.
Am I on the right track?
Kind of as I see it, yes. Not sure about witness style scheme and security. Sounds like a weak point at first, but it's the strength and feature of the system. You can conduct transaction without having to know the wohle picture. Think of a little IOT-device sleeping 10 minutes, waking up for 60 seconds, checking something (sensor?), doing transaction, sleep again. Kind of an offline transaction. This could not be done with a blockchain because the device would have to be online syncing the whole time. Or it would need a thin-client server structure, like electrum wallet. Plus you can do transaction without any cost whatsoever other than doing a little POW.
What came to my mind would be to setup some nodes in a LAN, separating them from the network via firewall, let them be on their own for 60 minutes and then reconnect them. Transactions should be valid. Not sure sure about coordinator needed at this point in time, but if finalized, things like that should be possible.
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