Issue:
Unity posts warning messages to the console about UV Overlap even though my models do not have overlaps in their UVs.

Resolution:
This is most likely the intended behaviour of Unity. The "overlap" that Unity is referring to is not "chart overlap in UV space". Instead, it is the "chart bilinear neighbourhood overlap in lightmap space". In other words, Unity detects an overlap whenever texels in two lightmap charts are sufficiently close to each other to affect each other's bilinear sample values. In such cases colors from one chart may "bleed" into another.

Because this distinction is so subtle, we wrote a docs page about this:
https://docs.unity3d.com/Documentation/Manual/ProgressiveLightmapper-UVOverlap.html