If you feel a business rival would be that concerned about page rank, as opposed to anything that might conceivably be paramount to a real business -- then there's a more fundamental problem with the website.
And it's this. You see, if a business rival thinks that whatever information surfers are looking for on your site, they could find something "similar enough" on HIS website, then ... that's pretty strong evidence that there's nothing obviously unique about EITHER website. (There may still be something unique, but if so, it's not OBVIOUS.)
The editors are always going to focus first on sites with an OBVIOUS POTENTIAL for uniqueness (which is, again, not the same thing as uniqueness, but it's a very good first estimate.)
So what you should do is make sure that whatever uniqueness your site has, is obvious. That's your best route to influence the editors.