I know what you're trying to say, but your wording is off. Something cannot be theoretically impossible but practically possible.

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 :)

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.

Well, it's all about the implementation. In theory, the implementation is flawless. In practice, it never is. It's sort of like saying there is software with no bugs: It's exceedingly rare.