They could then generate a new key for site.com, trusted by browsers that don't support cert pinning, but yes, that new key for site.com would have a different

They could then generate a new key for site.com, trusted by browsers that don't support cert pinning, but yes, that new key for site.com would have a different fingerprint. The only way to keep the same cert fingerprint is to get site.com's cert's private key, either by demanding it with a NSL or FISA order, or by breaking RSA (2048bit, in most cases) if the site uses RSA as almost all of them do. Generating a new cert from a trusted CA would be caught by EFF's SSL observatory (an optional feature in the HTTPS everywhere extension) and similar efforts. It would fail if used against a site that has its certificate's CA pinned in the browser, unless the NSA gets the CA private key for the right CA. Therefore, if they do have CA root key(s), they wouldn't MITM all the ssl connections they can. They would use that capability sparingly.