Yes, exactly, it's the same thinking that lets the government search people's houses when authorized, or detail and question them when authorized.

We already have this concept of "the government can go through your stuff" in the form of search warrants. It's not a leap at all to apply that to encryption, too, even if some specific law gets it wrong at first.

I'm sure if pocket enigma machines were around when these laws were first being put to parchment, there'd have been something in there about encryption from the start.