Q: Steering wheel vibrates while braking.

The people you talked to were all correct in a way. With an unbalanced tire, you will not feel the vibration at slow speeds. You will only feel it once the vehicle gets faster. It sometimes goes away with increased speed. A warped brake rotor will cause vibrations when you try to slow the vehicle down. It generally gets worse as you drive faster, but can almost always be felt, even at lower speeds. If you feel the vibration without using the brakes, suspect the tires being out of balance. If you feel the vibration at almost all speeds during braking, the rotor being warped is likely. A certified technician, like one from YourMechanic, will be able to diagnose this vibration and determine what repair is needed.