Also, perhaps terrorist networks target people with terminal illnesses and nothing to lose? Or perhaps the FBI is worried that someone who has been denied treatment in the US will turn terrorist all on their own. We have a large population that has been wronged by the system and has nothing to lose, I think the FBI wants to keep an eye on them. I know, FBI!=NSA, but the whole "parallel construction" deal shows exactly what they think about separation of powers: at least a few of them see it as an obstacle to overcome, not as a safeguard against abuse. And a few people is enough to do all the damage in the world.
Also, let's not forget there's a heavy financial incentive for individuals with access to such a database to sell the info to insurance companies. It follows that such individuals then have a motive to push for the establishment of such a database. They could launder the info into some "proprietary liability metric" which they would be able to sell for loads of money. I don't know what internal checks they put in place after Snowden but they can't be perfect. Any shadow copy of your health records increases your exposure and provides an opportunity to the unscrupulous if the records can be accessed in aggregate.
In your last scenario, the "bad" agents only win if they can sell the service, but keep secret the inputs to that service. I'm sure they can do that in the short term, but it's quite likely that eventually a salesweasel will speak a bit too freely in a semi-public forum and the whole scheme will unravel. After all, other government agents would be pissed off, if only out of jealousy.
and
http://en.wikipedia.org/wiki/Infection_control#Isolation
especially if "terrorists" are anywhere within the many small-networks lurking in all that data (http://en.wikipedia.org/wiki/Small-world_networks)