Seems reasonable to me. They need to be careful about how they make health claims. The Quaker Oats people and a number of others have it down to a science: Just say it "may" have positive health benefits. It's all in the wording.
There are lots of studies that show lots of things. After all, graduate students have to do something with their time. It's clear from the letter that FDA did do a proper thing in this case. It's their job to police health claims.
By the way, walnut oil is horribly toxic to some, and is used as a permanent hair remover by others.
Claiming that a single ingredient is a typical marketing tactic for people wishing to promote health claims for their products. There are a lot of outrageous claims out there, and the FDA has a mostly good history of policing them.
End result of this is probably that Diamond will simply re-word their claims and everything will be cool. They have good products of high quality, and they are reputable.