The FBI initially thought that all three shots hit. That may have been based on what the Connallys said and the evidence that the last two shots were closer together. They appear to have accepted that the shots were spaced like this:
FBI agents Frazier and Simmons did their shooting tests with Oswald's rifle with targets spaced at 175, 240 and 265 feet based on the evidence that the last two shots were closer together. This timing difference also made sense to them because the change in shooting angle between 1 and 2 would have been greater than between 2 and 3 so it would take longer to re-aim the rifle between shots 1 and 2 than between 2 and 3 (Simmons 3 H 444):
- I should make one comment here relative to the angular displacement of the targets. We did not reproduce these angles exactly from the map which we had been given because the conditions in the field were a little awkward for this. But the distance--the angular distance from the first target to the second was greater than from the second to the third, which would tend to correspond to a longer interval of time between the first and second impact than between the second and the third. The movement of the rifle was greater from the first to the second target than from the second to the third.
Then Agent Frazier became an expert on human anatomy and decided on his own, apparently, that JBC was turned too far around by z240 to have sustained his torso wounds so he must have been hit by z235 or z240 (3 H 170). By that time they had done a botched recreation (using the Queen Mary security car and new full spring foliage on the oak tree) and concluded that the first shot occurred no earlier than z210. This was a problem because there was not enough time between z210 and z235 for Oswald to have fired two shots.
So, Arlen Specter came up with the SBT to solve the problem. It was not based on evidence. It was based on opinions that conflicted with the evidence. It was, according to Specter, based on the assumption that JBC had been hit by only one bullet and the absence of any indication in the car that the car had been struck by the bullet that exited JFK's throat.
But this presented a huge problem trying to reconcile the evidence of the Connallys (supported by others such as Gayle Newman and Dave Powers) that JBC was not hit in the back on the first shot but was hit by the second shot several seconds after the first shot was heard. Connally had a clear recollection of the impact of the second shot which occurred after he heard the first shot, recognized it as a rifle shot and turned around trying to check on the President. Since there were many witnesses who said that JFK reacted to the first shot and this appeared to be corroborated by witnesses who could identify the location of the President at the time of the first shot, and because of the 1.......2....3 shot pattern, the first shot must have gone through both men and the Connallys were simply mistaken. This was certainly the view of John McCloy.
Of course, the WC left it open as to which shot missed (a necessary consequence of the SBT) while acknowledging that there was quite a bit of evidence that each of the three shots did not miss. Of course, three commissioners (Russell, Cooper and Boggs) never accepted the SBT.
Then the HSCA came along and decided that the first shot was around z160 and missed and the SBT occurred around z190. This left only about 1.6 seconds between shots. And, of course, there was the problem that they also found there were 4 shots and a conspiracy. However, SBT proponents were happier with the conclusion that the first shot missed because that meant that Governor Connally had not been hallucinating about being hit seconds after hearing the first shot. It didn't fit with Nellie's evidence, although it did fit with her sense that the first two shots were closer together than the last two (contrary to many more witnesses who recalled that the last two were closer and in rapid succession). So Nellie was right on the spacing of the shots but wrong on seeing JFK reacting to the first shot. And the rest of the witnesses could just be ignored.
But the HSCA conclusion of 1.6 seconds between the first two shots was not a good fit. Once the acoustic evidence was (correctly) discredited, SBT proponents were free to conclude that there could have been a longer space between 1 and 2 - at least enough time for Oswald to have fired the shots. Then came urologist Dr. Lattimer who added two more letters to his degree to opine as a neurologist that JFK was assuming the "Thorburn position" beginning at z226 - a condition that he opined (contrary to facts of the case that Dr. Thorburn had written about) would occur milliseconds after suffering a spinal impact. Of course, the absence of any evidence did not deter the well-intentioned Doctor. He then noticed the change in position of JBC's jacket relative to his shirt and concluded that this was a lapel flip caused by the bullet passing through his chest etc.
The opinions of Dr. Lattimer were met with relief by SBT proponents who could now say that they had scientific evidence that JFK was shot at z223 and that the bullet went through JBC. This was very satisfying because now there was 3.5 seconds between the first and second shots. The spacing between the three shots was now more than enough for Oswald to have fired all shots.
Then came Bugliosi. He was skeptical of the Lattimer "lapel bulge" and mentions it only in passing in footnotes. He concluded that the SBT shot occurred at z210. But that still fit with Oswald firing all three shots.
So, it appears to me that the single bullet "fact" has had a long evolution and there are still different conclusions among SBT proponents as to what that "fact" is.