Some of the confusion here might be from not clearly understanding the terms. An Arc has a radius, it is a section of a circle. When you start with a 90˚ arc and move one end of it, SketchUp tries to preserve the arc, so the result in your second example is because you have made a 90˚ arc larger in size, so it’s radius must also grow to stay an arc. See how when I inference the second example with the line tool the inference engine still shows me the center of the arc, and not with the third example? Your third example is part of an ellipse, it does not have a set radius and so cannot be an arc. Here, I take the second example which is still an arc and recreate a circle, this would not be possible with your third example.
The distortion you see is because the radial degrees of the original arc you start with is preserved.