See the paradox? It's impossible for them to do my Day 3 transaction if my Day 1 transaction was purged from their platform as promised but fully capable of performing such due to some b-code. Ergo, if there's no record of the first transaction, then it's highly probable that one could obtain coins that they didn't want to be attached to. It can't be 100% possible to have it both ways.
I do see the paradox, yes. I'd love to hear their answer. I have the intuition that hashes could form the basis of a system which partially answers the question, but I don't have it all worked out.
Day 1: Bruno sends me coins from address 1, I hash "
Bruno@mail.com" and "address1" (separately) and concatenate them to get the "bitmixer code"
Day 2: ...
Day 3: Bruno sends me coins from address 1. I need to make sure I don't send him any coins that came from previous addresses from Bruno. I hash "
Bruno@mail.com" and get the first half of a "bitmixer code". I choose an address to send him coins from by excluding any candidates which exist in my DB of bitmixer codes where the first half of the code is hash(
Bruno@mail.com).
I agree that it seems that they have to be storing something, in my sloppily constructed example a list of bitmixer codes which are a hash of a username and an address. I suppose that as long as they don't store the actual username they can claim they don't have a record. Anyway, I hope they answer your question which was very well put.