It seems there is some confusion here about my question let me try to be more clear.
If I use the Tor browser or serf of some coffee shops free wifi or whatever so the IP is not at all traceable back to me and make a payment to someone that has no idea who I am, and I do not give any personal information at all, and I make the payment using bitcoin, is there any way to trace out my legal identity only using the information from the bitcoin payment?
even using tor here are three ways to track you
1. you use a coffee shop. some how the agencies track the tor nodes back to the coffee shop, ask for their CCTV, use face recognition software, blah blah blah
2. you get busted by the police for a unrelated crime, they take your computer, scan it and find your public addresses that you use. they then match that to other transactions. blah blah blah
3. you do a private deal with a shady person involving delivering products to your address. the other party is actually a police officer in a sting investigation.... blah blah blah
bitcoin is about as anonymous as cash, it all depends on how you trade with it and what kind of information you pass long with it. if you have a pocket full of cash and you do a deal infront of CCTV, your at risk. if you do a deal with an undercover cop, your at risk, if cops raid your house and find related cash from another crime, your at risk.
simple answer is that bitcoin is digital cash, no credit card application forms, no Bank ID required. but still not 100% anonymous
i do not condone illegal activities but the way mixing services work is simply depositing funds into a exchange and then withdrawing, chances are you don't get the same coin back. much like buying a TV from a store, never unboxing it and then returning to a different cash register in the same store for a refund