You are saying that Google might ban a company because its site contains links to some other site? How is that possible? Almost every site on the web has at least one link to at least one other site.
Based on what you've said, I can't see any reason for your client being banned because of what what is is proposing. But it won't do him any good either. Given that the fourth site only contains one page, and that page only contains links to the other three sites, then the fourth site will never show up in a search, and no external site will ever link to it. In other words, it will have no value whatever.
As for the question of whether each of the businesses should have its own domain, that depends on how the client want to brand his business, and how the visitors view the relationship between the businesses. In other words, it's a business decision, not an SEO one.