On reflection,I don't think I've ever taken anything to the cleaners that was folded or on a hanger. I just grab an armload and then dump it on the counter,and ask when I can come back for it.
Same with me. Although I suppose at some time or another they sort through it and put the identifying tags on it before they mix it with all the other clothes. Seems that whoever did that at the cleaners would have seen the stain at that time. Who knows if they would remember something like that with the volume of clothes that goes through a cleaners every day. However, I did have a shirt returned to me from dry cleaners one time that had a note attached saying they were unable to remove a stain. Lo and behold, there was stain on the front that WAS NOT there when I dropped the shirt off. Naturally I claimed that they must have been the one to cause the stain since I didn't point it out to them when I dropped the article off. Guess what? They replaced my shirt.
Maybe the cleaners. I always put 'em on hangers (they'll charge you 10 cents extra unless you return them), the clerk counts the items and looks for tears or missing buttons.
Never found any bloodstains though ...