To further your point, even Snowden didn’t have access to the documents that tell us precisely what BULLRUN is able to do, or how.
(The speculation is, of course, with reasonable circumstantial support, is that it is a ~$1B program that has brute-forced the most common 1024 DH group in use.)
We simply don’t have the hard data, it is (educated) speculation based on what information we do have.
Even the existence of the program is TS. Its capabilities remain secret, due to the exact system you describe.