Kinda, the problem is once you've moved through a couple wallets (many wallets, in the case of the mixing services), it becomes very hard to tell the difference between one person moving their coins around, and one person paying another person.

    A --> B


    A --> B --> C --> ...--> Z

Pretend you know who A is already. Who are B through X? Is the person in control of A also in control of Z? Or any of the other wallets? These are answers the blockchain doesn't give you.