I gotcha now. We're talking about two different parts of the oversway. The leftward shape I was describing is normally taken first, and then the rightward shape. I never mentioned the second shape because I thought it was more likely that you were misinterpreting the first shape, as opposed to omitting it.
With the Waltz example, the text you quoted actually describes the second half of an oversway (sometimes referred to as a "drop" oversway). What they've done here is put step 3 of a Closed T-mark in place of the first shape.
The reason that this particular example works is because the third step of a T-mark is actually very similar to the first shape of the oversway. The most notable similarity is that your left side is projected forward on both. The man's hips on a T-mark rotate slightly farther than his top, opening the position up to PP. Whether you turn your top to the right or your base to the left, you end up more or less in the same position.
In the Tango example, I'm not sure what figure leads into it, but I'm assuming that it's a left-turning figure such as a Closed T-mark or Left-Turning Rock (Reverse Pivot). Again, we're looking at the third step of the figure being a sort of an alternative to the first shape, which is still ultimately almost the same thing.
You have to realize that the first shape is basically an over-swayed promenade position, and as such it has many of the same principles. The man's shape in PP is such that his left side is projected forward. The simplest way to achieve PP, then, is to have him rotate his left side forward... in other words, turn to the right. But it is possible to turn to the left to PP, as in an Open T-mark. In this case, the man's base will turn more than his top, leaving his left side projected forward.
I probably should have also mentioned that when turning to the right the top will rotate more than the base, but I was trying to avoid too much detail. It was pretty complicated already.
Anyway, my suggestion to you is to try learning the static entrance (movement straight to side, body turning right) to get a feel for the first position. This sets you up beautifully for the drop part of the oversway. Then later on down the line if you want to enter with a left-turning figure, you have experience with the proper leading shape.
When you do try the Waltz or Tango example, stop on your third step and check your shape. Your left side should be projected forward, and sway to left (both looking in PP). Now you're ready to take the second shape.
Enjoy!
Sincerely,
Jonathan