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Something that could be a factor:If the rings are not truly co-axial,there will be some tube distortion when the rings are tightened.
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I don't think so.
If the scope tube's clamped tight in rings, it doesn't matter how much distortion the tube has changing the optical alignment of the lens groups that might be caused by the ring's axis and alignment with each other. It's repeatable from shot to shot and doesn't change by ajusting anything; elevation, windage, power of focus things. Ring mechanical axis and centering with each other perfectly only happens when both rings are first installed on the bases then lapped with the right size tool to 100% exact diameter of the scope tube. Or, with adjustable ring sections that first align with the scope tube then on the tube's axis in them as the rings are tightened on them.
To say nothing about what happens to aluminum scope tubes when rings are overtightened on them. Some folks have epoxied their scopes in rings to ensure the rings don't squeeze the inner mechanics rendering the scope towards bad stuff. Most epoxies will release their bonds to metal when frozen and changing rings on such a scope means it spends a day or two in your freezer.