If you know what you are doing you can lift the flat tire by the axel clamps and by the spring shackles. When I mentioned this to the TT dealer they agreed but it is a big "IF".
From the dealers perspective, the new TT owner with a flat tire could be really upset, super excited or just plain all thumbs when it comes to mechanics. So, they just tell everyone to put the jack on the frame.
My TireAid works but it will sink into softer ground without a board under it. I do not know how well it works with wide spaced tires or triple axles.