I'm active in a number of locations on the net, including my own websites. Bitcoin has become the currency of the Internet, and I hope that I can persuade more buyers of domain names to use it for payment. Bitcoin Talk is a great reference for potential users, and thus a good credit rating here could be important. Obviously stating that I am DT1, when due to a lottery, this is no longer true, diminishes my credibility. Potential buyers will obviously wonder what I have done to lose my ranking. Perhaps it is time to use a more accurate name for the system. The alternative is to remove oneself from the rankings, but this seems to be counter productive for every one concerned.
You could just say that you're a member of Default Trust. But in general using it as some sort of "credit rating" is wrong IMO. Being in Default Trust means your judgement is trusted. It doesn't necessarily reflect your creditworthiness or other attributes that are important in trading. That's what trust feedback is for, which doesn't depend on you being in DT1 or DT2.
Whether that matters at all outside of Bitcointalk is another story. Someone coming here and claiming they have a reputation on some other site where we can't verify it, or even check if the reputation/account may have been purchased, would be treated with great suspicion. I would imagine same would apply in reverse.