Disclaimer: I'm not the expert. So this is just more rambling, really
My thoughts: Yes, it may be better to find your real max with an all-out effort, but it's not a clear answer. First, it may not be medically advisable for some people to perform at that high of an exertion level. Second, it's more accurate to use an all-out effort in something that is a slow-twitch fiber aerobic activity when done at lesser intensity, like running, cycling, or rowing, and gradually increase the intensity (after a proper warm-up) until you are going at high intensity, as hard as you can go. You will get a different result if you begin too quickly as with an all-out sprint, or if you tire yourself out before you get to max intensity by ramping up too slowly. Third, it will vary with how many muscle groups you are using and how much lactate you are producing (related to fast-twitch fibers, I believe... so, more lactate and lower max HR with something kettlebell-related like swings or snatches). So for a max, I get something like 170 with snatches, 175 with cycling, and 180 with running (while 220-age = 172...so, a decent approximation, for me). The scenario you describe above sounds right, Steve, but that was a lot of years ago, and your max likely has gone down a few bpm since then as it does tend to decrease with age, even for the fit.
As for finding the max HR at which you can train aerobically, this is relative to building your aerobic base, or slowly building the amount of work you can do while remaining aerobic, with minimum glycolytic fueling. Yes, other protocols will benefit the aerobic system also. What he mostly talks about is a way to focus exclusively on the aerobic system, stimulating primarily mitochondrial development in the slow-twich fibers, which is the biggest part of the aerobic engine... in my understanding. And is a lower-stress (i.e. healthier) way to train the majority of the time. So for the training that HE recommends, yes, don't train above that. But that's one of many types of training; and further, one of many types of aerobic training. So overall, no, I don't agree that we should never train above that MAF-predicted HR. I'm not sure Maf does either, but I'd have to re-read the bigger context in his books.
So overall these two things -- max HR and max aerobic HR -- are two different things, and not actually much related or relevant to each other.