No, the rest of the paragraph makes it clear(?) that the user who created the transaction can show it was them.

I don't understand the math at all, but the claims on Zerocoin are rather strong. But it does depend on a high enough volume to hide in.

People pay a large premium, like 10%, to get anonymous BTC, as evidenced by the "cash by mail" prices on Localbitcoin. (Other methods are even more expensive, but that's usually due to risk of default/reversing - like taking PayPal or gift cards). If you control the supply of Zerocoin then it's basically a license to print money.

Zerocoin is really what BTC needs to increase volume, I hope[0]. This is assuming most people care about buying BTC anonymously, out of the people that profess to get anonymous BTC. I tried to buy truly anonymous BTC last year. Things I compensated for:

- Physical evidence (fingerprints, hair, face/body recognition) in every transaction - much harder than it seems!

- That means wearing gloves when getting the cash out of the bank and exchanging $100s for change at stores. As well as using double bags when transporting the cash. This raises lots of suspicion.

- Also means you cannot: Deposit cash for BTC (bank video) or meet a seller in person (obvious, yet often recommended on BTC forums).

- ATM/Bank teller note serial recognition. Wells Fargo claims they don't do this[1] but it is too easy and makes too much sense. This means going to the bank to get $100 bills, then changing them at shops. (ATMs only provide 20s, making it much more difficult.) And even then, you'll want to use a shop with high cash turnover.

- Handwriting. Easiest way around this is to ask a stranger to help write for you, faking incompetence or an injury.

- Stamps: Buying from the USPS is actually very difficult. The automated machines only take traceable cards. Video cameras are all over the place. Fortunately there are plenty of third party sellers that'll hand you a couple of stamps for a few bucks.

- Location. This is the hardest to conceal. If it isn't clear, the only way to buy BTC anonymously is wish cash. And since you don't want to meet in person, cash by mail. (A dead drop is a possible alternative, but further constrains your location and is far easier to be recorded (like leaving cash in a locker).) I went to drop off my envelope in an out-of-the-way USPS mailing box. But that still gives away my location generally. To be extra paranoid, one must consider all USPS mailboxes to be monitored (video surveillance), and that USPS mail recording will know which potential mailboxes were used for any given piece, along with some time window. Involving a stranger is a good idea, or perhaps leaving the envelope at a hotel/concierge.

Even with all that, one must assume that your general physical location has been leaked. If you need to make multiple purchases, this leaks a lot more information, as it shows where you were over time. (I travel a bit, so if I bought whenever I felt like it, that pattern alone would narrow me down to a few hundred thousand people, perhaps even less.)

Zerocoin promises to eliminate this info leak as well as Tor eliminates your IP. It's got a huge potential.

0: Edit: It's not that I'm some kind of BTC believer. I actually find most "true BTC" users to be morons. But I think it's a good thing because it provides a way to force a partial step back against government invasion of privacy. The mere idea that most people consider "money laundering" to even be a thing, let alone something bad, just shows how far the government has corrupted people's minds.

1: The teller gave me a fake $100 note. When I went to return it, the manager said he had no way of verifying. OTOH, I guess they would say that, regardless.