Welcome to the Q&A Forum

Sounds like nonsense to me, do they give any evidence to back this up? I cant see how you can dilute a keyword, besides linking out with the keyword. The reason people like to keep to one keyword per page, is that there is only one page title, one H1(should be only one), one url, not because more then one will dilute the other, and especially in your case, I cant see how the same keyword can dilute itself. Don't keyword stuff of cause, but you are far from doing that.