Oswald in the doorway: the blog of the Oswald Innocence Campaign, by Ralph Cinque

This schematic shows where everyone was in the ambulance, and as you can see, there was no room for Graves- unless he rode on the roof.

And thanks to Amy Joyce, we can see exactly what happened. After Oswald is settled in the ambulance, the Bieb goes to the right middle door and gets in, and you can see him descending into the vehicle. 

After that, Dhority and Leavelle climb in the back, and the tailgate is closed. And then, Graves walks down the length of the ambulance on the right side, passing the spot that the Bieb got in. Graves does not get in; (there is no room for him unless he should sit on the Bieb's lap). Instead, Graves goes past and walks around the front of the ambulance to get to the police car that he will take.

He has gone past the door that the Bieb entered. Graves is walking around the car. We don't see any more after that; there is a break. But, that is what happens.  

In his testimony to the WC, and at the Ruby trial, and in other public statements, Graves stated that he rode in the ambulance with the others. And that was a lie. If you think it's a small thing, you're mistaken. This was the fatal shooting of the man who purportedly shot and killed the President of the United States, changing the direction of the country and the course of history. Arguably, it was the most crucial and pivotal historical event of the 20th century. So, every detail of it was important. Graves lied to cover something up- something that must have happened on the way to the hospital.

And the fact that he overtook the ambulance is very disturbing. He certainly didn't chase it down and overtake it. How fast would he have to drive to overtake a speeding ambulance? And why would he do it? Why was it necessary or even helpful? There was no advantage. Ambulances speed to hospitals all the time without police escorts. The fact that Graves wound up in front means that they must have stopped somewhere, after which the order got reversed.

Now, we have to start examining the times that were involved, starting with the only official time that we can be sure is accurate, the time that Oswald was pronounced dead by Parkland doctors. That time was 1:06 PM.  You still think they got him there by 11:30? I say: not a chance.