Limited Dissolve changes vertex positions? Carry over from a youtube video comment here
In the video, the presenter manually fills in an example with edges to make faces. A commenter suggested using Alt-F to fill and then Limited Dissolve to reduce the mesh. As this is a video on precision modeling, I was surprised to see vertex positions of the bevels and circles on a simple 10mm plane with 4 holes were changed.  Is there a way to dissolve edges without changing vertex positions?
Blend file for reference; 1 degree + 5 degree dissolves

Edit: Thanks to Robin and taking a second look, I realize now that Blender uses single precision floats instead of double... so that explains my scripts output differing. Don't use 5 degree (default?) with Limited Dissolve and you get great output.
Thanks to Robin, his script, and taking a second look, I realize now that Blender uses single precision floats instead of double. In the first python script, it is printing whatever python thinks (double precision).

Don't use 5 degree (default?) with Limited Dissolve. This lead to original vertices being deleted.
Less than 1 degree limited dissolve doesn't have this problem.