You are right that SketchUp behaves quite oddly when it comes offsetting and follow-me-ing curves. The convention for segmented curves is that the vertices should be on the curve which also means the offset distance should be measured vertex to vertex on a curve. This is the convention SketchUp uses when displaying arc radii in Entity Info. However, SketchUp doesn’t care of whether edges form a curve and just offset them as if they were straight edges, meaning the offset distance is measured perpendicular to the edges, not vertex to vertex.
By rotating the circle as Jim suggested and having “half” a segment at the ends you can work around this issue. However it means it’s now the midpoints of the segments and not the vertices (endpoints) that represents the curve. If you are interested in making precise models this means the radius in Entity Info now isn’t to be trusted since it’s measured vertex to center point, not segment midpoint to center point. Instead you manually need to scale the arc to the desired radius using scale tool (if you care about this precision).
I suppose there is also a plugin out there with an offset and extrusion tools that honors curves and creates gives the expected result but none that I know of.