I think the point of a mixer is not to give a person 'clean' bitcoins but to avoid the coins being traced back to their original owner's address (to hide the source of the money, in a way). Of course, the money you get might actually be somewhat 'tainted' (but you'll get small amounts from different sources) but the transactions will be confusing enough to count as untraceable. As for getting 'clean' bitcoins, I think I've seen stories that some actually do that by paying more to get freshly mined coins which literally don't have a history.