If you read the webpage carefully, you will see that:

1. Only when redeeming on BR, QR, MH, VS or 9W, you will not be able to mix carriers. You use the same chart based on the distance, but you will only be able to use just one carrier throughout the itinerary.

2. When redeeming on Star Alliance, you can mix and match any number of carriers as you wish, or use one airline if that's what you want. You use the distance charts as above.

They even give you examples of what can be done on the page you linked to...(VS="Partner Airline"=VS only in itinerary, Star= SQ, UA, NH in one itinerary). Just because they give you an example of mixing carriers on the Star award, it doesn't mean that you have to use more than one airline on a Star award - it's just an additional option for your convenience.