The black hats are fedoras, and are worn by Hasidic Jews. I don't know any Reformed or Orthodox Jews who wear those. Hasidism is generally thought of as the most Orthodox of all Jewish groups, and I can't imagine a Hasid eating in a non-kosher restaurant.
The Fedora is only one item of clothing that identifies a Hasidic Jew, the other would be the white shirt buttoned to the top, black suit jacket and dress pants, and prayer shawl. Additionally their facial hair is very distinctive, and varies depending on if they are married or not. Like I said, I can't imagine a Hasidic Jew eating in a non-kosher (treyf) restaurant anymore than I can imagine someone from management not recognizing a distinctive manner of dress belonging to that religious group.
IMHO, something's just not right with this picture.
Anne