Logged as a bug:
nHair Start Curves near the borders of polygon shells apparently have incorrect NURBS parameters. This means that the Paint Follicles Tool does not work correctly on these clumps. No solution except to delete the follicle.
Add nHair to a polygon object with open border edges. Attempt to use Paint Follicles Tool. Notice that follicles at the borders are not affected. Make Start Curves visible. Select the problematic Start Curves and look at their nurbsCurve shape node attributes. Min/Max values are 0 and 4, and Spans is 4. Select any of the Start Curves that are responding correctly to the Paint Follicles Tool. Look at their shape node attributes. Min/Max values are 0 and 1, and Spans is 1. Note: rebuilding the bad curves does not seem to help. The only solution I have found is to delete the errant follicles.