When you thought that, you should have felt a great sense of shame, and a desperation to find the truth. The question is not how things appeared to you, it is how they should have appeared to you, and you did not recognize this failure. I have noticed this a lot on the internet, people seem to think they are right but they forgot somehow, what it took to get to this point.
The general principle being that the form changed over time. First, in history, we know that the form was changed over time. Grasp Bird's Tail, obviously, is a derivative of Lazily Arranging Clothes. Therefore as an obvious point GBT was created as a derivative to more closely mirror the push hands sequence. This is a common feature in Chinese martial arts, teaching a two person form first by teaching a kind of frame that has to be learned before the contact sequence. In fact, this idea solves the whole thing. You can even go all the way back to Jiao Ti/Jiao Di (horn butting) and you will find the rudiments of these kinds of martial arts. In fact, most Chinese martial arts come out of the rudiments of this kind of practice.
It's hard to say more without rambling, but if you study the history of the art's development you may see the same process repeated. I think the story of how Yiquan was created is another great example of this process.