He also decides to ask Parker's opinion of the manuscript since she is the one who has the greatest expertise. It might be interesting to modify the scenario a bit and explore whether changes in what Slater tells or shows Parker change one's conclusion regarding the appropriateness of his action. For instance, Slater could have asked Parker for her opinion on a small part of the paper without actually showing her the manuscript or telling her why he was asking. Or he could have shown her only a portion of the manuscript, perhaps the Results section but not Methods. It is not easy to determine whether Slater should have shown the manuscript to Parker in any circumstances, with or without the editor's permission.
Conflict of interest is involved as well as confidentiality.
As soon as Slater tells Parker about the manuscript or shows it to her, she has new information that will affect her behavior, just as was the case for Slater opening that envelope in Phase 1. It is likely that she will push harder to finish her experiments and prepare her own manuscript. However, while Slater was able to choose how far he read, and thus how much he knew about the competition, before he stopped and possibly contacted the editor, Parker has less freedom to choose. Once Slater asks her to read the manuscript, it may be difficult for Parker to tell her adviser that she doesn't think she should read it, even assuming she is aware that there could be a problem. Thus, Parker is pulled into an awkward situation through no fault of her own, but rather through Slater's decision.