What exactly is being kept secret, though?
As to the brain, is it not simply the case that it was returned to the family for the funeral or afterwards as it's just the right and proper thing to do? Looking at it sensibly, why on earth would there be a reason for the national archives to keep it? That just seems bizarrely ghoulish, to be honest.
What would it prove in any event? The Zap film proves conclusively that it was a shot from the back to the front. The shot which came out of his neck and also hit Connally was also fired from the rear. There is literally no evidence anywhere of any other shots being discharged.
I get that people have questions, questions which derive from the absolute enormity and the graphically public nature of the event. I get that people have trouble accepting that such a thing was possible by a single man acting alone. Now, don't get me wrong, perhaps he wasn't acting entirely alone and perhaps he really was the "useful idiot" manipulated by other actors. That is a different set of questions, though - and still ones I really don't see much evidence for, speaking personally.
You cannot argue with physics, though. The two bullets which hit Kennedy (one also hitting Connally) were fired from the rear. That isn't in dispute. The probability that they came from anything other than the rifle found in the book depository is so remote as to be effectively impossible.
The study of ballistics is pretty well defined and straightforward when you consider that it is all about the physics of a given, specific round with known powder weight, known bullet type and weight, consistently loaded, and fired from a rifle with a known barrel length and rifling twist rate.
All that, coupled with known weather/wind conditions and consistent shooting by a skilled shooter, can allow for accurate predictions and results. When any of those factors vary, so do results. Hunters, military snipers, competitive match shooters, and ammunition reloaders know these things very well.
When trying to forensicly reconstruct a crime, such as the shooting of President Kennedy, it is TERMINAL BALLISTICS, which are used, and that is a much more unpredictable and widely variable area.
When a bullet strikes something, many different things can occur. The many studies and theories about the Kennedy assassination bear this out. Besides the two bullets usually mentioned and ascribed to Oswald's WW II Italian Manlicher Carcano rifle, there was at least one other round (and possibly more) fired.
The Warren Report concluded that the first shot fired by Oswald missed, possibly having been deflected by a tree branch and hitting pavement next to, or behind the Presidential Limousine. That bullet was not reported as being recovered (although it may have been). Kennedy can be seen in the Zapruder film reacting to the first shot - either startled by the noise or possibly being struck by a fragment.
The second shot (according to the Warren Commission) struck Kennedy in the back. There is controversy here. While the official WC report concluded that it exited through his neck and then struck Governor Connally, medical witnesses state that the back wound was only a few inches deep. Former Secret Service Agent Paul Landis came forward just last year to claim that he found the so called "pristine/magic bullet" in the Limousine just behind where Kennedy was sitting and that he placed it on the table in the Emergency Room.
There is much controversy about the third "head shot" bullet as well. There was an apparent bullet strike dent in the interior windshield frame just to the right of the rear view mirror, as well as a crack in the windshield just to its left (as seen from the driver's perspective. And yes, the bullet fragments reportedly from that shot ( linked by the FBI to Oswald's rifle) were all found on the floor in front of Nellie Connally's left side jump seat.
The body itself would have to be considered as the primary source of forensic evidence. The rushed manner in which the President's body was taken from Parkland Hospital in Dallas, and autopsied at Bethesda Naval Hospital in Maryland without communication between doctors at those locations added controversy.
We will probably never know all the answers, but there are many legitimate questions.