Yes it is true - and for two reasons: 1. when silver comes in contact with stainless steel it causes an electrolytic reaction that will cause the silver to tarnish however, 2. washing silver in a dishwasher is always a bad idea regardless of the other contents because the heavy chemicals in the dishwashing detergent can harm the silver either through the nature of the chemicals themselves or their reaction to the hot
water and the other metals in the dishwasher causing a solution that is caustic to silver.