I will try to take a screenshot the next time I am working on a model.
Maybe the surfaces have 3 vertices, but 2 of them are in the exact same spot, somehow?
EDIT: I believe that is indeed what they are. To test... draw a triangle, then move one of the vertices to the exact location of one of the other two. What you have now APPEARS to be a line, but it's actually an "invalid" polygon. However, the "select invalid poly" tool won't select it.
(It's difficult to see here, but it's just to the left of the axis indicator.)
Note: I don't do this intentionally, but it's extremely common to have these "left over" invalid polygons when working on models, doing various operations, etc.