940 non-turbo

Car shudder with shaking steering wheels at between 60-80 km/h speed. Took it to the wheel and tire shop. Advised to do a balancing job on wheels. No improvement. Then the suggested that rotor could be warped, so did both front rotor skimming. I'm not sure if this is the right term but what they did was having some kind of device attached to the rotor that sufaced the rotor as it turned. The idea was to even out the disc surface that was the cause for the shudder.

After that job that took about an hour, the "on the road" test came back with steering wheel still shakes (but with slight improvement). Those guys there told me to have the back rotor skimmed too as the remaining vibration is caused by warped back rotor. I argued that shudder in front so obviously has nothing to do with the back rotor. They explained that because the back rotors were tied to the axle that has no free play, the vibration is transferred to the front, and the only possible area that could release the vibration is through the steering wheel.

I had my doubt, and told them that I'll come back the next day because it was getting late.

So, is what was told facts or fictions merely to rip an ignorant soul like me?

Help, as I feel really unsafe driving in a shaky situation like mine. BTW I had the back caliper serviced for a stuck caliper recently.

Thanks as always

Laozong