What is the validity of the statement made by one who says that a woman whose husband has passed away should not go out for four months, and that only close relatives should see her, including her maternal uncle's sons and her husband's brother's sons?

There is no difference between a woman in her 'iddah (waiting period) and others in terms of dealing with men. Her mahrams (unmarriageable kin) are permitted to enter upon her and speak with her. Non-mahrams are not permitted to mix with her or look at her hair, and so forth.