Comment by anamexis

And likewise, it's not particularly meaningful to say "That's a consequence of not being allowed to put yourself in check (by any means)."

The rule, "3.9.2: no piece can be moved if that exposes or leaves its own king in check." covers both the case of moving a pinned piece as well as moving the king into check, i.e. it covers all "means" of putting yourself into check.