Everyone's seen the video of President George W. Bush taking the mound at Yankees Stadium on October 30th -- in the wake of 9/11 -- but the man who caught the pitch is telling us what went down behind the scenes.
TMZ Sports spoke with Todd Greene -- the backup catcher for the Yanks that year -- who not only praised Bush for throwing a strike with the world watching ... but doing it while wearing a bulletproof vest.
The Yankees were taking on the Diamondbacks in Game 3 of the World Series -- the first World Series game back at Yankees Stadium .