My opinion is that pulling the beaver too tight will sometimes rip the edge of the pelt when drying. Of course raising it on the nails helps as the nails will tilt inward.
I beleive it is difficult to prove how much if any that it may thin the under fur by pulling too tight. Besides visual and size measuring the beaver is graded for quality by feel of the fur between the shoulders of the pelt. This is where the density of the underfur is checked.
Trappers for the most part, specially if they sell to country buyers, have only seen beaver graded by size, leather color, and visible damage. It takes years of experience to be able to grade fur density by feel.
"It's what you learn after you know it all that really counts."