While the 5D MK III is obviously superior for tracking birds in flight, I recently found a batch of old National Geographic magazines from 1916 in with some old things I had bought at a estate sale.
There were plenty of sporting events, wild life, and even birds in flight.
So, its a matter of skill and perseverance. A 6D is incredibly more capable than what they had to work with in 1915 or earlier when those photos were taken. Its really just a matter of skill and practice. You can let the camera do it all, or you can learn to get by with a bit less automation. You can get every bit as good of photos, its just more work and requires more skill and understanding of the equipment.
I'm not down on anyone using the best AF available, I have and love my 5D MK III, but I feel that I could get the shot with less capable cameras as well, its just more difficult.