The salesman who sold me the race helmet at the Triumph dealer is a racer and was trained to fit lids by the Shoei or Arai helmet representative. He said the helmet should fit snug so the stress between the head and the helmet is distributed over as much surface area as possible when you crash.
Arai makes helmets for all sorts of head shapes. He found one to fit my noggin. Then, he showed me how to tighten the strap. He said to tighten it enough so the helmet does not move around when I go into a crouch. His reasoning is that if I get a hit from the front, side, or rear, most stress will be on the side of my head and some will also be distributed to the top. That stress distribution away from the immediate area of the contact patch is harder to obtain if it is loose.
As tempting as it is, it is not wear a helmet loose, I am told.