[inerte]

Don't worry, your wording is also off, something can be theoretically impossible but practically possible. Things can not be impossible but also practically possible, but for every theory disproved, there was a contrarian thing possible :)

[orblivion]

I suppose it depends on the context. The only way this could happen is if you're talking about a bad theory. Whereas something theoretically possible can be practically impossible, even for a good theory, if real life situations can't match the conditions of the theory.

In this case the NSA didn't even do anything theoretically impossible. They did a workaround. They added backdoors, which violates the conditions of the theory. It's like saying I got through your unbreakable door by coming in through the window.