Some ringing is always present, with every headphone... That said, not everyone is sensitive to it and not always it is significant enough to become bothersome. I know how ringing sounds like... It can be pleasant (Denon D7000's midbass), bothersome or completely fine/acceptable. It's a purely subjective thing unless it is VERY present - like with HD700.
To sum up, I really doubt there is no ringing with your pair because of the way K812 are designed - just look at the image of K812 cups from the inside - the same design as with T1 or HD800 (without dust covers) = no dampening. There is a hearable ringing in treble with T1s and HD800 w/o dust covers as well. I do not find it bothersome (I actually prefer HD800 without the dust covers as it improves sound significantly) but it is there and I am able to hear it occasionally, depending on music or condition of my ears (fatigue etc.).
Edited by HeadNroll - 2/6/14 at 1:18pm