Cossette was invited to a session of the Legislative Assembly of Ontario in 1980 during a special week-long debate on Canadian federalism and Quebec sovereignty (this debate occurred against the backdrop of the first Quebec referendum on sovereignty). In his comments, he said that he did not believe the claims of friendship and brotherhood for Quebecers that had been expressed by Ontario legislators. He was quoted as saying, "We simply hate each other traditionally, and it shows. You can hear it, you can feel it." These comments were criticized in "The Globe and Mail" newspaper.