I was told if I only changed the pads and not the rotors it would cause the car to vibrate when braking
The vibration, if it happens at all, is due to piston run out. The further the brake piston moves out of the caliper, the looser things get and so when rotors are turned the pistons have to travel out of the caliper assembly slightly further, but it's a very minute distance. I don't blame jag for throwing rotors at every job as they have nothing to loose, and it's less of a chance someone will come back complaining about who knows what. That being said, if the rotor has a number stamped on it's edge, that number indicates the minimum tolerance that it can be turned to. Jag brakes aren't magic nor are the cars. It's just a car and just a brake system. If the car has some specific rotor protocol, then I'd follow it, and maybe the SVR's do. I have an S and the brakes are likely a Bosch system. It's a normal brake job except for a procedure to deal with the electric packing brakes in the rear.