Social Security Questions? Ask a Social Security Expert
Although it is true that she cannot "double dip" she is entitled to receive a benefit that is the greater of her own benefit (based on her earnings record) or his benefit. Social Security has responded in a vague and confusing manner here and she should appeal their decision.
Additionally, she is also entitled to a death benefit as his widow. While not large every penny helps. She should apply for that if she has not yet received it.