What cut of beef is "fillet of beef"?
I believe it's another name for the tenderloin. http://www.recipes4us.co.uk/Beef%20Cuts.htm

Also, if you check out this other fillet of beef recipe from the same show:
http://www.foodnetwork.com/recipes/ina-garten/fillet-of-beef-recipe/index.html
You can see a much better picture of the meat. That one is clearly a tenderloin.

So The Fillet Mignon is part of that technically...