In order to assess who is correct the exact nature of the tire needs to be seen in more detail. If the tire has been damaged by driving, a crash or some other method, than Technician B would be correct because the tire would need to repaired. However, if tires is moving funny as a result of a bump or some other impact to it, then it could be that the weights have become mis-aligned and then Technician A would be correct in that re-balancing solves the problem.