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?
For full nodes it's not true. The scalability doesn't come for free, you have to pay with increased confirmation time.
Right. Because in a traditional blockchain so many transactions are clumped togather, the security that you purchase for your own transaction is also a 100% positive externality on every single other party in your block. With a the "tangle" style chain the security externality takes time to propagate out. Its a logarythmic process but even those start out slow. The advantage being, however, that you don't need to concern yourself personally with every transaction. Only the ones relevant to your transaction. The ones that reference you after the fact up until the point that you feel satisfied with the level of security and the history of those units in particular to check for doublespends.
Sorry if I missed this in the whitepaper. But you cant be scaling well if everyone is monitoring every transaction. Necessarily. That is the problem that needs to be addressed for any decentralized ledger system to scale truly well. So the problem here is that what if someone sends you iota and you dont happen to witness that transaction. Does the sender personally send you a reference to the transaction?