Bad spackle job on wallpaper

My kitchen (late 90's contruction) has wallpaper that was glued to wallboard. I know this because all homes in my neighborhood have had same and I learned this when I had a bathroom remodeled. The bathroom, I had all the wallpaper removed, areas were spackled/sanded/ painted and is perfect. Since the bathroom was done several years ago and is perfect but was expensive for the small area, I knew as large as the kitchen is I needed to check see my other options. Two months ago I hired painters to paint my home interior and to paint over the wallpaper. I was told they would tear any lose areas, spackle the torn areas , and spackle the seams. They applied kilz and 2 coats of paint. Once the work was completed, there are large areas where the spackle was not smoothed and the areas are very visible. Several seams have areas that were not been spackled. I called the owner of the company, he came to the house and said they don't do drywall (which is odd since their invoices also mention wall board and the fact they took the job saying they could do it). I am at a loss with messed up kitchen walls and will be out even more expense to get it fixed. The only thing the owner offered to do is to repaint once I have the dry wall repaired. At this point I am not sure what is my best course for repair- I am concerned with the wallpaper on wallboard, the spackle, the kilz, and 2 coats of paint what will happen if someone says they can sand the areas and repaint. Any input regarding this will be greatly appreciated.