I don't know what they mean by double handling but I suppose that's what you are referring to when you have said they should be capable of standing comfortably and unaided.
I thought both dogs in the clip in your link looked awful. More like hyenas who slink along rather than, what I think of, as a GSD.
There are two issues, I think. Quite distinct. The conformation of GSDs with the exaggerated sloping hips, which in the extreme results in dogs that can't stand straight, can't walk without wobbling - and which probably genetically have poor hips, resulting in a higher incidence of displasia in their offspring. This has been an ongoing welfare issue since the 70s, and the continued failure to address it effectively is one of the reasons a lot of people still give the British Kennel Club a bad press.
So, ludicrous though it would seem that being able to stand unaided needs to be specified in a breed standard, it's good to see the KC taking this step, since it seems that the breed folks are unwilling and/or unable to sort out the issue themselves.
The double handling, as Annie says, is there being some one outside the ring attracting the dog's attention. It seems there is also a thing about running the dogs two at a time, and fast - the implication being, to me, that all techniques possible are used to encourage the dogs to move, and to look as though they are comfortable and able to move.