The phrasing in this sentence (the use of the words "his" and "him" is the standard way to use correct pronouns which refer to an indefinite (and always singular) pronoun such as "anybody." In today's world, however, it's seen as sexist since only the masculine pronoun is used, thus seeming to assume that only a man could be that "anybody."
Better to fix it by using plurals:
The article pointed out that people who can get their doctors to meet them at the offices are fortunate.
