Bucketstove. gotta ask cause I'm always asking why, and ~24 is seriously different then ~34/6. Your post is new so my brain is trying understand why delta between pivot and edge angle. Part of me suspects the angle cube's gyroscope is not fully implemented (hows that for stubborn minded- gish). Is it possible to just tell us what happens when holding angle cube like it was a pin-wheel pinned to stone, in cubes center, so cube stays in vertical orientation, freely rotating left of right movement and visa-versa, the stones plane?
It's not related to the implementation of the angle cube. The reason is purely geometric. If the cube is oriented perpendicular to the cutting age (tangent line), you read the sharpening angle. If not, you read a meaningless value.
Besides the simplest cases, an angle cube rotates in all 3 axes. If we think about the angle cube in aviation terms: the pitch is used for measurement of angle; the taw is your "a pin-wheel pinned to stone" that also affects the reading and should be used for perpendicular orientation to the cutting edge; the roll - I'm not sure about other cubes... the gauge in my photos (post 51) ignores rolling.
A couple of images from my old article. The cube aligned to the guide rod measures the purple angle.
All we need is the correct orientation of the cube - perpendicular to the cutting edge. You don't need to remove the cube from the sharpener like in
bucketstove videos.
Better yet I think I just had a good idea! How about think of this question by replacing the stone arm with a plate of glass on the sharpener that freely pivoted at the same spot. Now lay that plate of glass on the knife like your going to sharpen it. How well does it contact? I think pretty good, and no angle change as you move away from the center since it is a flat plate of glass that pivots freely in the middle. This is an interesting question since the whole point of a guided sharpener is accuracy and consistency.
If you take EZESharp, clamp one of your knives with a straight portion, and put a plate of glass, you will be very surprised.
Your glass plate will have full contact with either rail OR knife, and 1 point of contact with the knife/rail respectively.
Your real environment is not spherical chickens in a vacuum. You've made the assumption "plane and the knife edge lines up", but you cannot do such assumptions. You can project a plane through two lines in 3D space ONLY if two lines are parallel. Who made them parallel, you? No, you did not mention anything like that. The rail and the knife will be parallel only if YOU make them parallel - by reclamping and/or rail calibration. EZESharp does not have rail calibration...
It's very naive to believe that a consumer mechanical device with all built-in tolerances and a knife with all imperfect geometry can be aligned in 3D using only human eye and human hands with such enormous precision so they will be parallel.
There are hundreds of cumulative effects that don't let edge and rail be parallel.
And again - what for? Fixed pivot units keep a constant sharpening angle for any straight portion of the blade. Mobile pivot unit on the rail promises constant sharpening angle only for one straight portion of the blade that will be parallel to the rail.
As folks have discussed these different aspects of these pivoting-arm sharpeners especially EP, I've been following through the thread discussion, putting long straight or curved blades on my Apex, demonstrating to myself the various points that that have been made. And was able to demo this too, that the angle on the portion of blade that's centered on sharpening table doesn't change even for EP settings that are higher or lower than the 21 dps where it's perpendicular. I only tested at the extremes--10 and 27--but that's enough to confirm to my satisfaction your updated point. 
