I understand, three shots is an accepted fact but should it be. Studying witness statements is a quagmire because of witnesses with multiple statements.
Yeah. An incomprehensible quagmire. Just look at this and try to figure out how many shots there were:

The eyewitness vs earwitness comparison becomes a tedious argument, but there is physical evidence that helps explain what happened.
https://www.history-matters.com/archive/jfk/wc/wcvols/wh26/html/WH_Vol26_0243a.htm
The shell casings actually provide physical evidence of how many shots were fired. Who noted the evidence was Josiah Thompson. In his book "Six Seconds in Dallas" he states he viewed over thirty shells that had been fired in the carcano (chapter VII footnote 4 of Six Seconds in Dallas). All the shells had an indentation in the side of the shell casing except for CE543. In the book is a photo of the shells together and notation showing the position of the indentation on CE544, CE545, and CE141 (the unfired cartridge), but not on CE543.
Of the three shells and cartridge shown, the most telling is CE141 for the reason that indentation is there but the cartridge was never fired. Why that is important is in the FBI memo from Hoover to Rankin, the indentation in the side of the shell casings is referred to as a "chamber mark." It is a mark that is produced by the rifle itself due to a manufacturing defect. The "chamber mark" is only produced by the rifle when it is fired and expanding the shell or in the case of CE141 when the chamber of the rifle is expanded due to the heat generated from the rifle having been fired. CE543 does not have the "chamber mark" and among other things exhibit evidence of having been dry fired or basically was being used as a snap cap.
I am not sure what evidence you are referring to. It was determined by the FBI that all three shells had been fired by the C2766 rifle to the exclusion of all other rifles. This was determined by matching the bolt-face and firing pin impressions on the shells with the bolt face and firing pin of C2766 (per: Frazier, 3H416-417). (A snap cap does not recoil back against the bolt face). All three shells are shown to have bolt-face impressions matching C2766. This cannot happen if the shells are from unfired cartridges. Here is an excerpt from the WC testimony of Supt. Nicol's of the Illinois Bureau of Criminal Identification and Investigation (3H505):
Mr. NICOL. Based upon the similarity of the firing-pin impressions and the breech-block markings, as well as ejector and extractor marks, it is my opinion that all three of the exhibits, 545, 543, and 544, were fired in the same weapon as fired Exhibit 557.
Mr. EISENBERG. Mr. Nicol, did you take photographs of the various shells under the microscope?
Mr. NICOL. I took photographs of the specimen which I referred to, or was referred to, as Q-48, which would be this.
Mr. EISENBERG. Yes. That is Commission Exhibit 545.
Mr. NICOL. These were also taken under the comparison microscope in the same fashion as the other specimens.
Mr. EISENBERG. And these were taken by you?
Mr. NICOL. These were taken by me.
(3H508):
Mr. DULLES. What is 543?
Mr. EISENBERG. 543 is a shell found in the TSBD building.
Mr. NICOL. This is a photograph I took of the head-a portion of the head of Q-6, or Commission Exhibit 543.
Mr. EISENBERG. May I have this admitted as 619, Mr. Chairman?
Mr. DULLES. It shall be admitted as 619.
(The photograph described was marked Commission Exhibit NO. 619 and received in evidence.)
Mr. NICOL. It might be well to introduce these, too. These are the same as the ones which are mounted, except that I have cut them for the purpose of matching them.
Mr. EISENBERG. I would like to introduce these two photographs-also taken by you, Mr. Nicol?
Mr. NICOL. Right.
Mr. EISENBERG. Which are similar, or taken from this photograph. That will be 620 and 621, Mr. Reporter.
Mr. DULLES. Exhibits 620 and 621 as described will be admitted.
(The photographs described were marked Commission Exhibits Nos. 620 and 621 and were received in evidence.)
The microscope photos showing these markings on CE543 provided by Nicol (CE619-621) show conclusively that CE543 had been fired.
AND, since there was no empty shell in the rifle when it was found, this means the all three must have been ejected from the rifle chamber.
Nicol also found that the shells had several markings that indicated that, as full cartridges, each had been loaded and ejected at least 2 times before firing and CE543 had been loaded and ejected at least 3 times. This was determined that CE543 had a magazine follower impression made by the Mannlicher magazine on the last bullet in the clip. So this means that CE543 had, at one time, been inserted as the last bullet in the magazine at some time. Since it was not the last bullet in the clip on 22Nov63, this means that at some time it had been part of a clip of bullets in the magazine and then had been removed without firing.