I think the biggest question here is How long did the Secret Service have this guy in their sights before firing at him ?
Watching the video as it happened you hear what seems like Five shots which is what the redheaded witness said, then three shots a second later, I assume those three shots killed the shooter. If that second group of three shots killed the shooter he had to have been in their sights already, it was an instant response without the time required to acquire a target. If that’s correct the Secret Service waited for him to shoot first! Allowing him to make his attempt at killing President Trump.
I read it exactly as you do.
Someone must have told Ss don’t shoot first.