It's hard to tell from the picture but your fuzz looks like a film of connective tissue. You often see this tissue in suet, which is the hard fat surrounding the kidneys. When you pull suet apart with your fingers, thin sheets of this stuff stretch between the pieces. If that's what your fuzz is, it's normal.

Edit: Here's a picture (second one down) of the membrane that surrounds suet. If this link breaks, Google "pull off the papery membrane".

http://jennifermclagan.blogspot.com/2009/02/suet-dont-waste-it-on-birds.html