Co-operation? I highly, highly doubt that.
I can see only two possibilities for how the NSA could collect every single phone call of an entire country, such that the Washington Post would agree not to publish the name of the country. One is that it's something like North Korea where the infrastructure is really weak and there might conceivably be only a handful of points where all telephone calls pass through. If a covert team on the ground were able to splice those fibres, or hack the telephone equipment remotely, and somehow duplicate the internal traffic onto fibres heading out of the country , I can see they could be intercepted at that point.
The other possibility is that it's a small country that's supposed to be "allied" (Washington does not really have allies), like Belgium, seat of the EU. We know that GCHQ hacked Belgacom pretty badly. Undoubtably the NSA has done the same with other telcos. In this case, the WashPo agrees not to disclose it to avoid causing even more severe diplomatic fallout (though this was apparently not a concern so far). For a small but modern country it's quite feasible to imagine hacked telephone equipment simply sending all phone call data out over the internet or a fibre that's meant to be dark without anyone actually noticing, as phone calls are relatively low bandwidth.
Regardless, this is pretty amazing. Every time I think these fuckers can't get any creepier, they do. First OPTIC NERVE and now this.
These stories always leave me depressed. It's clear nothing is going to happen, the politicians all seem to be creaming themselves over these powers and can't wait to legalise it all ... then they can conveniently go after anyone who is breaking their collection with crypto.