I can see you never sat in on a military aircraft loss accident investigation board
The A4 Skyhawk association (among other sources) memorializes Fred White as the pilot whose aircraft was hit by the Zuni. I would suppose they are privy to the facts.
Why would McCain need to claim this for himself and not even mention LCDR White? I can only think of two reasons, neither honorable
http://a4skyhawk.org/content/forrestal-fire
In your link it says that White was in a aircraft hit by the rocket not that it was the only one hit. I suppose they memorialized him because he died and not McCain because he didn't. It also says 132 people died when all other accounts say that 134 died so I guess even the A4 Skyhawk association can get things wrong.