What do you mean DT?
DT stands for Default Trust members. They are a selective group of people who are in the Default Trust list of every user. Long standing of this forum has shown that they are trustworthy in forum deals and thus the name.
Anyone can put a feedback on your profile and as long you have a negative trust there some opportunity here that you can't join because they don't care where your negative feedback came from.
First of all any person
can post feedback on your profile. That does not mean that the feedback needs to be accurate. People who still have some common sense will actually try to investigate any reason behind the feedback and if there is none they would ignore it. Those feedback remain under "Untrusted feedback" and wont show up unless clicked on.
On the other hand feedback from a DT member will be fairly correct and will show up as "trusted feedback" on your trust wall. Although this is subjective still they wont give you a negative trust unless you do something seriously bad to the forum like cheating campaigns with alt accounts, scam someone, buy/sell forum accounts.
I believe you are coming to this opinion from getting rejected from some bounty campaign, which in that case you just have to accept and move on. Such bounty managers are not doing their work properly if they are not looking in the reference of the feedback. But do care to link it here?
P.S This thread belongs to "Reputation" not "Meta"