Ok, this PDF is saying what I've been saying. The two parts are indicated by the upper and lower stems.
Just because they may have the same note, at some point, you still have to indicate who is singing the note AND for how long.
For example, on the first page of the TW-PART WRITING paper (pg. 86) after the paragraph that starts, "When both parts are written on the same staff....", in the sixth measure you see the upper and lower melody playing/singing the same note. BUT, the lower melody is playing/singing the note for 2 beats, while the upper melody starts on that note but moves on.
And, in that same example, in measures 7 & 8, both melody parts are singing the same note for the same amount of time; BUT, it's still two parts. Without the stems, one would think it was simply one part.
Understand?