That's what I always assumed. But it's easy to test: change the depth to 1, and see if
my feedback changes. I just tried: it's the same. So ";dt" works as expected and has nothing to do with your personal settings.
I things we clarified everything now

Thank you, LoyceV!
You're overcomplicating this

I was also thinking that I am doing this while writing my post

The purpose of ";dt" is to override any of your personal trust settings and show the ratings how they would look like to a newbie who just registered on the forum (or anyone who doesn't have custom trust settings).
Yup, correct, that's what I knew.
Not sure what you mean by "real" score but it sounds like it's the same as ";dt".
And yes, this is what I meant:
By "real" score I mean the score seen when adding a ";dt" at the end of the profile URL.
And as LoyceV said, it is always depth=2 because that's the default setting for new users. That's the "specification" you're looking for.
Thank you suchmoon, now I understand better. In conclusion, any DT1 and DT2 can alterate a user's (real) Trust score, but DT 3 and DT4 can't. And DT2 are able to as by default the Trust depth is set to 2.