A) They did show 'proof' ostensibly, to the specific agencies of interest i.e. UK/Germany.

B) Your 'a' and 'b' are missing the most important point, in that the revelation of their knowledge may compromise some ongoing intelligence program. The information may very well have been provided by spies who'd be put at risk.

Literally yesterday WaPo published a story on the most comprehensive US intelligence program ever and it quite nicely illustrated the challenges of how to reveal how much you know, and the consequences therein.

This is not 'open source land' where we like complete transparency, it's a different game.

C) There's also another issue, and that this may not be 'black and white'. For example, the ostensible 'back door' may not be clear cut: it may be that it doesn't yet exist, but there are elements in the design prepared for backdoors to be very easily added at a later date.