Well damage is an overstatement, you scuff the paint to allow for the bedliner (paint, primer, etc) to adhere. It requires minimal damage and could be buffed out after the required sanding if you changed your mind. So damaged is a little over the top as well as "sanded down very well" when the instructions just require a scuff.

As for the air chisel, even at an angle you are going to go through the paint in many places requiring much more work after. You cannot apply the bedliner to bare metal so any places where that is present you would need to prep and at least prime the area.

However, to each his own. Either method is going to require work so whichever the OP cares to do