I think the difference is their goals. The DTI tries to ensure that there are no changes to significant events in their known historical records. The Krenim however, are willing to change known history to benefit themselves.
In a sense, the Krenim are trying to do a similar thing with regard to changes. They are trying to correct for a mistake they made and are trying to restore their timeline. It's just that the Kremin don't care who they erase in the process of restoring their own timeline. DTI is, at least, less prejudicial in globally preferring the "prime" timeline.
At any rate, goals aside, doesn't the DTI have to own up to similarly troubling effects?