Nearly all of the arrests in the WOT have been announced late. Padilla's, for example. The reason is that you don't want your enemy to know who've you've got until he gets a lot of bogus info from that person's "replacement." Or until you get a few mails and calls from your prisoner's handlers. Not to mention, you want time to interrogate him before the ACLU and CAIR try to get involved.
According to the articles, Yee had been under surveillance for quite some time, so toting the papers out of the country wasn't the tipoff. Not to mention there seems to be some reason to believe he has actually been observed passing info on to others.
I wouldn't be surprised if he's "Mr. Unnamed Source" in a number of screeching-harpy articles on Gitmo from the likes of the UK Guardian.
Unless of course he was discovered based on items learned from the capture of say, Syrian or Ansar operatives, or intercepted messages concerning people the bad guys shouldn't have known had been captured yet, etc.
As for the prisoner's cooperation levels, by some accounts it hasn't been very good of late. And if one guy is helping the prisoners coordinate their chat, the info would be vey "cooperative" but no doubt misleading anyway.
Sending him off to a Navy brig is an indication that this isn't just some unfortunate misunderstanding.
BUT, on the more POSITIVE side, here's another possibility that I don't think has been brought up :
Maybe some recent additions to our little collection of terrorists at that brig haven't been cooperative. Given the nature of what those jokers were apparently planning to do, I don't blame them. Maybe we want them to be more cooperative. That particular cell of people has been in the news of late with Shukrijumah sightings popping up too, indicating there may be a live al Qaeda team on the loose.
As for those detained, I'm sure they would find it much easier to get comfortable and chatty with a nonwhite Muslim chaplain who is accused of being in their camp, and who faces serious charges.
Why send an Army chaplain to a Navy brig, the very same one as is housing some of the very worst of the worst we've caught so far?