Q. I am formatting my MA thesis using APA, and I have found conflicting information about the literature review section.

I'm not sure if I am in complete understanding of your questions & also am not sure if I am over-thinking it.

There is a "rule" (or conventional wisdom, at least) that everything your read for your thesis should be included in your works cited. However, in the body of you paper, you only need to cite what you sum up, paraphrase, or quote that is the work of an author.

This is from the Publication Manual of the American Psychological Association, 6th edition ...

When to Cite
Cite the work of those individuals whose ideas, theories, or research have directly influenced your work ... the number of sources you cite in your work will vary by intent of the article. For most articles, aim to cite one or two of the most representative sources for each key point. However, because the intent of a review article is to acquaint readers with all that has been written on a topic, authors of literature reviews typically include a more exhaust list of citations (p. 169).

I am not sure what you mean by "the entire review is of one author's single work." I think of a literature review as examining the works of many authors addressing a topic to determine the extent of knowledge on a topic, gaps in the knowledge, contradictions, and future directions.

There is another piece of conventional wisdom that says APA bows to local custom. Therefore the ultimate arbitrator of how to address this question would be your thesis adviser.

Good luck.