All brake rotors get rusty. That is completely normal so ignore? that comment from the mechanic.
The rotors are more than likely warped but depending on the vehicle’s mileage a loose wheel bearing or suspension component can also cause a brake shudder.
If the brake shudder is pretty severe, and depending on the type of vehicle, chances are you would need new rotors IF the shudder is rotor related. Rotors can be machined but in severe shudder cases this usually means they would have to be turned down thinner than what is acceptable. This is a safety issue so they are better off being replaced.