At least in this case, YouTube seems to be following the DMCA's notice-takedown-counter-repost dance. Fourteen business days (512(g)'s outer limit) from my counter-notification, I received this email from YouTube:
In accordance with the Digital Millennium Copyright Act, we've completed processing your counter-notification regarding your video http://www.youtube.com/watch?v=a4uC2H10uIo. This content has been restored and your account will not be penalized. For technical reasons, it may take a day for the video to be available again.
The NFL has apparently chosen not to sue to keep the video offline. Once again, therefore, viewers can see the NFL's copyright threats in all their glory.
I'm left wondering how many other fair users have gone through this process. On Chilling Effects we see many DMCA takedowns, some right and some wrong, but very few counter-notifications. Part of the problem is that the counter-notifier has to swear to much more than the original notifier. While NFL merely had to affirm that it was or was authorized to act on behalf of a rights-holder to take-down, I had to affirm in response that I had "good faith belief that the material was removed or disabled as a result of mistake or misidentification of the material to be removed or disabled." A non-lawyer might be chilled from making that statement, under penalty of perjury, even with a strong good faith belief.
Thanks for all the comments!