Tires: Tire shimmies, camry 2002, vibration problem

Question
I have Camry 2002. Put Yokohama 215/60R16 tires on it.  Now, after a year, the car vibrates when braking at low speed.  I asked mechanic to balance the tires; he said that the balancing was good, and vehicle need new tires because of the shifted belt.  How dangerous is that; do I need to replace all tires or just one, and how to determine which one?
Thank you

Answer
Michael,

The vibration problem is in your brakes, not the tires - probably a warped rotor.

BTW, belts don't shift, but it is possible that you have some irregular wear - which the mechanic is interpreting as a shifted belt - and that is caused by misalignment and aggravated by insufficient inflation pressure and insufficient rotation practices.