The focus sensors do not sample in a very tight 'spot' manner. Their radius extends a bit further out of their respective brackets. Also the corner ones sample only towards the inside of their corner (top right samples only left and below). Top and bottom ones behave similarly. This way you can get an idea where your autofocus system searches to achieve optimal focus.
It may happen that optimal focus is found a bit closer or further ahead than the exact point you are aiming at, especially if you are over it and observing at an angle so that contrasty/textured stuff slightly in front or behind it are in the sensor's radius.
Try doing the same tests by focusing on objects, letters etc placed on walls or some other place that is going to be perpendicular to the lens axis. And of course, you can always shoot a test roll and see who is right, the split image or the autofocus system?
Finally, I think the F6, like most modern cameras, needs a good matte focusing screen with random grain, like the B2 for the FE/FM series... the plain B screen is ok but it is optimized for f/2 onwards and might also produce moire on very fine detail...