Using Paint version 6.1 (Build 7601: Service Pack 1), Windows 7
Steps to reproduce
Save As monochrome bitmap (.BMP)
Click on Pen to draw lines (Left click to draw black, right click to draw white)
Drawing white does not work.
Found a work around by changing the properties to color, doing the edits, then changing back to monochrome before saving.
But this is not a preferred solution and not appealing to an end customer, my preference is to fix the issue.