Rule 3.9.2: No piece can be moved that will either expose the king of the same colour to check or leave that king in check.
That's why treating colloquial concepts like "pinning" as though they are rules in and of themselves is not really precise or productive.
At the "Is this move legal?" level, they don't need unique rules of its own if the lower-level rules are specified correctly.
I was pointing out that that specific rule (read to mean that moving a piece pinned against a king is not allow) is not strictly necessary. Putting oneself in check is not allowed regardless of whether it's because you moved a piece that was pinned against your king or moved your king directly into the line of sight of an opponent's piece. These are the different "means."
As a sibling comment points out, "The only action you can ever take in chess is moving," so it's not particularly meaningful to say that the only way to put yourself in check is by moving.
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.
No piece can be moved that will leave the king of the same color in check.
While we're being pedantic though it's not a property of the piece that might be able to be moved that will place the king in check. It's a property of the move. For example we might imagine you have a rook between an enemy rook and your king. You can move the rook along the line between the enemy rook and the king, but not perpendicular to it.
The rule should be:
No move can be made where the moving players king is in check in the resulting position
Also, pinning can happen with pieces that don’t include a king, which means you can just move out of the pin and expose whatever other piece.
It’s just a chess tactic, not a rule. It’s like saying a chess skewer is a rule too.