That's what I first thought but are the brakes on he F4 really that good?
Definitely, but they don't even have to be.
Think about it.
Hes landing, so he is going to be light, relatively speaking and the CG will have definitely shifted forward to some degree. He will be coming in with a relatively high power setting (compared to landing on land where he could be at power idle at touchdown). If he is on the brakes at touchdown, those wheels wont turn over quick enough if at all and it would nose over quite easily i believe.
There is a video on youtube of a stearmen ground looping at DCA airport two summers ago. One of our museum members helped build that aircraft and was flying right behind the guy in his own stearman that flipped as it happened. If you watch the video, as soon as he touches down, its an instant flip of the plane just because of the momentum.