but when the results don't line up the way we would expect them to
Part of it is due to display mate using 3 different ways that it measured the device. So for max slider brightness, they list 410, 478, 523 and 600. The 410 is the closest approximation to the test that Anand runs (for which they list 359). That's a big difference, but you can see they're the closest to each other and the description of that value on display mate is, "This is the Brightness for a screen that is entirely all white with 100% Average Picture Level." The others are all reductions of average picture level.
So for this purpose ^^ the 410 value and 359 are measuring the same thing, and display mate shows it 14% brighter than what Anand displays.
Now, let's not forget that display had one test where they listed 600. That's a 46% increase over the 410 on the mode that we'd be calling an equivalent test to Anand's. Keep a hold of this point somewhere.
So when they find a range of max auto brightness, they provide a range. Between 569 and 1048. This range is accounted for because there is more than one test being conducted, as indicated above, and it means that the smallest of those, 569, is what we would expect with a "screen that is entirely all white with 100% Average Picture Level". Which is what Anand's measuring. And they came up with 577. Wow, that's only a 2% difference. That's why I believe they measured the same thing.
So why is 1048 listed? Because the peak measurement under which this range was created is "a screen that has only a tiny 1% Average Picture Level". In otherwords, almost nothing is happening except a tiny number of pixels going nuts.
But there is a more important statement on the display mate page that clues us in to something. "For 100% Full Screen White the Galaxy Note 7 is 2% Brighter" (than the Note 5). Well let's find out if Anand agrees. Anand shows the Note 5 at 566 and the Note 7 at 577. That's 1.94% different. Are we all comfortable rounding that to 2%?
TLDR
When used the way people use phones, on auto brightness in the brightest ambient light, the Note 7 is going to peak somewhere around 569 nits. Anand calls it 577. This data is corroborated by the similarities in the two sources listed above. Under extremely unreal conditions, it can light up a tiny number of pixels SUPER bright - but that's not what users will ever experience. It's about 2% brighter than the Note 5 in automatic mode.
And the iPhone 7 is about 22% brighter than that in automatic mode.