Yes, you're right....Fritz had to have let Day take possession of the rifle because Alyea filmed Day dusting the rifle with finger print powder behind the brightly lit west window. I'm not sure that Day ever relinquished total possession to Fritz... There may be some law that would have been broken if Day had taken his hand off the rifle...
Now let's Look at the practical aspect of this..... If Lee Oswald had been the shooter, what would his actions have been after he had fired three shots? In my opinion he would definitely ( by reflex action) have loaded that fourth round, and it would have been in the chamber with the bolt closed and latched. And therefore the rifle would not have been found with the bolt unlatched and about 1/4 inch short of being closed and latched. It just doesn't make sense for an assassin to stop loading his rifle in mid stroke.
I firmly believe that the rifle was simply a throw down gun and it was never fired that day....
I think that the sight of JFK's head exploding could have been enough of a shock (even to LHO) to make him just freeze in the middle of loading the next round. But, of course, anything we come up with is only conjecture.
Another, totally different, possibility is that LHO actually did complete the loading process of the next round and set the rifle down between the boxes. The first photos taken by the DPD reportedly show the rifle before anyone touched it. And the rifle can be seen in that photo upright. The Alyea film appears to show Day lifting the rifle from a laying down position. So it is conceivable that before Day lifted the rifle from the floor that either he or Fritz could have lifted the bolt handle into the up position by reaching between the boxes. I am not saying that that is what happened. Only that I think it is a possibility.