If it "hurt" the animal, the National Geographic Channel  would never do it, or get away with it, what with the millions of viewers.

I guess when animals can't shake it off they adjust to it.

After a drying from a bath, my dog comes eagerly to me for his collar to be put back on! Obviously he is adjusted to it. 

As if it's a piece of jewelry or a watch that he considers to be his.

Indeed he shakes the collar and tags when he wants us to notice he is waiting to be let out into the yard.