solid PTO shaft on 3 pt auger

You are correct, the PTO shaft has to change length on any attachment raised and lowered by the three point hitch. While you could design something that could use a fixed length shaft, it would involve making other components move, and would thus be more complex (read expensive) and thus not normally done, especially on commercial equipment. I'll add my vote to the shaft being stuck, or possibly mis-assembled by someone with no idea what they were doing. I'll be interested in seeing pictures of the parts in question.