The unlikely part is not that the US government agencies could get the private messages, it's that they'd jeopardize the whole system by letting regular border officers use it directly (instead of, for example, data-mining and send out no-entry-lists) and show proof of its existence to (foreign!) citizens.
I mean, I don't know why Snowden bothered to leak the info, if they're just telling any 18-year-old German girl about it.
To be fair, the NSA outcry was largely over the scale of the monitoring and the lack of warrants. However that doesn't mean that (other) government organisations couldn't approach Facebook with a warrant and request specific data, such as private messages from a suspect.
Assuming for the moment that this story did happen exactly as we're lead to believe (and I'm only making that assumption for the sake of playing devils advocate - I'm firmly on the fence with this story due to how sketchy the details are), then it would be very easy for the NSA to cover up how they had such data: "We'd been investigating her for a few weeks - here's a warrant"
I doubt they would even need a warrant, I expect facebook will roll over for even an administrative subpoena (which are signed by clerks of the court rather than judges and are essentially pro forma).
I mean, I don't know why Snowden bothered to leak the info, if they're just telling any 18-year-old German girl about it.