I would strip the factory material to avoid any de-lamination problems down the road.

If the original headliner material has the foam backing, then you should remove the original covering before proceeding with the change over.

Why?
1. The foam will most likely fail within the next five years and the headliner will sag.
2. The suede material is most definitely heavier than than the original material and it will cause the original to pull away from the backer board. (Gravity still works)
3. It is always a good practice to never cover over old material when installing new. Cutting corners will come back at you later and you may end up redoing the project at your cost if it fails.

The only time Ill cover over the existing headliner is if the car is new. 2 years old max. That Tahoe headliner is already 5-6 years old. You don't want to risk your reputation putting your nice work over top of a headliner your not sure of.