Cathy Horyn is known for her scathing reviews.
Oscar de la Renta is also known for not holding his tongue - remember the stance he took on Michelle Obama’s McQueen?
So of course it would be the two of them that would square off in a match of calling each other names(hot dog for Mr. de la Renta courtesy of Horyn and hamburger for Horyn courtesy of Oscar). This is indeed professionalism at its best.
** in case you cared: I took “Mr. de la Renta is far more a hot dog than an éminence grise of American fashion.” to mean that Oscar is far more of an American tradition/past time/comfort than an innovator/influence on American fashion. Also éminence grise connotes influence.