Yes, they actually think people will confuse a whiskey with named 'Duke' with a picture of John Wayne carrying a rifle with the university.
John Wayne Enterprises (JWE) has sued Duke in response to the school's efforts to block attempts by Wayne's family to register the moniker for use in naming alcoholic beverages (with the exception of beer):
"Consistent with its policies and in order to prevent tarnishment of its brand, [Duke University] does not permit use of confusingly similar marks associated with unapproved goods or services, of uncertain quality and/or unregulated by [Duke University]."Apparently the two sides have done battle over JWE using 'Duke' for naming all sorts of things while Duke University has tried to protect it so they could the same (including food and beverages).
In a nut shell the argument seems to break down to this: the school doesn't want to be associated with alcohol sales and doesn't like the word 'Duke' being used to do so. JWE is countering by saying there is no way that can happen:
"Apparently, Duke University believes that products bearing John Wayne's world-renowned image and signature, like the bottle of bourbon depicted in Exhibit A attached hereto, will somehow be confused as being associated with Duke University...."Here is what a bottle looks like:
|via The Guardian|
Awesome westerns maybe, but not college.
[Guardian, Hollywood Reporter]