When i equip the rebreather my defense stat will fade bewteen DT and DR in the same way a weapons stat fades bewteen DAM and DPS, try looking at it for a bit and see if it fades from one to the other.
DR definately still has an effect, even if a DT greater than 0 is needed for a merchant to fix it. DR reduces the damage you take, once the armor is penetrated. DT is a threshold to overcome. Like bullets bouncing off the walking tank of Power Armor.
DR 85 for example will reduce damage you take by 85%.