I can't help thinking that Bill Clinton said this because he really doesn't want her to be president (although he can never say that publicly or privately).
So he decided to take the opportunity that Rove's statement presented, and made a statement that would sound like he is caring and sympathetic and coming to her defense, where really he is just casting further doubt on her health.
One of the comments on the NY Post side was that Bill is looking to take over for Hill like Eleanor did when FDR became too ill.
So, she has this history of a concussion, she gets elected, she gets ill, and Bill steps in to “help her”, since “helping” is a non-elected position.