She IS a carrier, but she is perfectly free of the disease. There is no contradiction between them. Because it's sex-linked recessive, Mary should have both alleles of gene H, meaning the father is sufferring from the cancer as well. Her brother is lucky because his X chromosome is from the normal allele of the mother and the Y chromosome(no gene H) from the father.

If the mode of inheritance is recessive, it means one allele of dysfunctional gene is not sufficient whereas dominant means one mutated gene can dominate the phenotype.

the disease is recessive, no symptom, quite right.