Yeah, he wasn't joking.
It also depends on the AF system in the camera. I had immense difficulties shooting an air show with my D5000 back in 2011. About 70-80% throw-aways for missed focus. No way to do the "pre-focus on a spot" at an air show, either.
Had a D7000 (same lens, though) for the 2012 show, shot 11 frames, not a single shot missed focus.
The other situations in your links, I agree with. Long exposure, low light, landscape, HDR, etc, focus manually (and consistently.) Giving it up for action shots, no way. Good AF can keep up.
As for "How does the camera know which kid has the ball?" you tell it. By pointing the one active AF sensor at that kid. That's what it focuses on.
Question, though. You say you're using a 40-year-old manual-focus film camera, and you're arguing against auto-focus. So what AF camera do you have that you've tried to shoot with in that situation? I'm asking because if you've not used AF, or have used AF on something like a P&S or a consumer-grade camera (like the D3000 or my old D5000) then you may be going on bad information. While I was using my D5000, I would have argued that AF was useless in action photography. My D7000 has told me otherwise.
Your camera has the split-image rangefinder in the viewfinder, so you KNOW when your subject is focused. AF cameras have ground glass only, no indication of precise focus. (Some have a focus LED that lights up, but you have to look around in the viewfinder and take your eye off your subject. Fast, precise manual focus is simply not possible with the OP's D7100. Your insistence that manual focus would be better for him is ludicrous, given what he's using. Also given what he's using, learning how AF works and knowing which mode to use, he should be able to get completely useful birding images.