I am on a roll with odd behaviors using the same basic shapes.
In the attached I have a red and blue close polysrf. If I boolean intersect the two, the red shape disappears and the blue appears to remain unchanged.
dear @miano
your details are less then 0.07 inches, your document-unit-tolerance is 0.01 inch.
normally your document tolerance should be at least 1/10 better 1/100 of the details you will model.
in general it is not a good idea to decrease unit tolerance (increase precision)
setting the document unit tolerance to 0.0001 and the boolean works … but the resulting data might be not suitable as steps before have been done with less precision.