They would in case they had freedom to rotate only, but unlike a centreboard, a pivoting daggerboard has freedom to rotate AND to move up and down like a daggerboard.

Summary:

Daggerboard - one freedom of movement - up/down
Centreboard - one freedom of movement - rotation on axis
Pivoting daggerboard - two freedoms of movement - both of the above.

Another drawing attached.

Cheers,
Luiz