A grey fox is just a color phase of a red fox, just as a cinnamon is a color phase of a black bear; so yes, it is a red fox.
Maybe in Alaska? But in the rest of the US they are 2 entirely different animals.........LOL
http://www.mass.gov/dfwele/dfw/wildlife/living/living_with_foxes.htm
I think you are confusing the term "Grey" with a Silver Fox which IS a color phase of a Red Fox.
I have a lot of experience hunting trapping and handling foxes, trust me that picture is a Red fox. When you learn the difference in builds and colorations they really don't look very similar at all. Sort of like standing a Mule deer next to a Whitetail.........to someone who doesn't know deer they are both simply DEER.
Just based on the body attitude, stance and leg length I can tell it's a Red fox even if you turned the picture black and white and cut off it's head.