I think of Grids (and the Hosts that populate them) as if SETI@Home hosted themselves at Amazon's AWS, and Amazon merged with AOL and AT&T. The core of the Host (the Foundation) is distributed across hardware owned by your provider (whoever owns the Grid your host is on - hosts exist on specific grids). They provide connectivity (wireless and backbone - AT&T); services, content, and experience (AOL); and compute power (Amazon AWS). But in addition to using their own compute power and bandwidth, every device also helps (SETI@Home or Bittorrent). Since almost everything is a device and has a processor, storage, and wireless, this adds up. AIs take advantage of this when they Emulate and since the Grid doesn't own the resources they are borrowing, they let it slide for the most part - especially since they effectively do the same to provide more power for hosts, etc.
Using what is today referred to as Fully Homomorphic Encryption, these devices can manipulate and process sensitive data without ever having it revealed to them, so it doesn't compromise the integrity of the host to have its functions distributed across unsecured hardware.
As for Foundations, I figure these are such massive conglomerations of data and compute power (not to mention learning algorithms) that they are effectively pre-sentient. So, taking that they are processing on highly parallel neural networks that have many significant parallels to the human brain, it isn't absurd to think that they would exist in a more or less constant state of REM like dreaming. Add to this that you are effectively mind melding with them via a direct neural interface, and YOUR sub-conscious would also help flavor how this all appears to you. You are drinking from a firehose and your brain is doing its best to make some modicum of sense of this over-stimulation.
So, yes, it's fantastical, but I'm perfectly happy to suspend my disbelief because Foundations are pretty awesome.
At least, that's my take.