We have several "industrial strength" prograsmmers here and see the same problem. Some chips (more for some brands than others) show "wrong device ID" and fortunately our programmers allow ignoring this.
I surmised that the problem is that reading device ID is done using extremely low currents. Based on that theory I tried cleaning the programmer socket till a shine and sanding the uC pins with extremely fine (800 grit) sandpaper. This made the ID read. This is as much of a "proof" for my theory as i can provide.

Erik