In this hypothetical scenario, it would all be dirty, but you would have no way to pinpoint which funds are associated with which illicit activity. At this point it becomes hard to levy any specific charges: "you are hereby charged with either breaking into a $100M bank vault, or fleecing grandma for $10, but we aren't sure which exactly."

In practical terms it might not matter, the funds would just be frozen. But it is still a form of money laundering that obscures the true source of the funds.