3D CAM paths are typically approximations. The amount of permissible deviation from the actual surface is controlled by tolerance. You can specify tolerance in Cutting parameters->stock (you've actually pre-specified this when you chose method)
There are also settings that influence accuracy of simulation. Adjusting these might make some of the perceived inaccuracies go away. There's always a trade-off; more accurate simulation is slower.
In my experience the actual cutting results tend to be better than simulation, as long as tolerance is set tight enough. You might like to google "chordal tolerance" to get an in-depth idea of CAM tolerances.
Our tightest tolerance for milling is +/-0.01mm, with a part stock of 0.5 and higher we increase the tolerance to +/-0.1mm, to speed up the tool path generation.
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You need to determine if the tool is really violating the part by .06, or if the report is due to tolerances.
Have you identified where on the part the system thinks the -.06 is? In show thickness, set the max to 0, and leave the min at -.06, to help find the area.
As suggested above, you may need to adjust the tolerances in the operation or verify to get a more accurate display and report from show thickness by color.