DW is an instability of a mechanical system that has a natural frequency of oscillation. Changing any part of the system can shift the frequency. A shift of one component can cause an oscillation in another component.
What you describe is very possible. Dampers do not cause or fix DW. DW is normally caused by a worn/loose/cracked component or mounting. It can be TREs on any of the joints, any of the bushings, including track bar and control arm bushings, or ball joints. I have even seen tires with a defective belt cause DW.
Double check for cracking on the frame rail where the steering gear mounts and the track bar bracket. Worn or oblonged holes can also cause problems.
The easiest way to troubleshoot is to crawl under the rig and have someone cycle the steering wheel back and forth while you watch each and every attachment point and joint for movement.
