I haven't worked at Amazon, and I won't speak to whether things are uncommonly bad there. Certainly Microsoft seems to have produced plenty of similar stories while escaping the broad stigma Amazon has acquired.
I will say, though, that I think your bad-reputation timeline is totally off. By the time that NYT piece broke, I had heard "Amazon is a horrible employer" from a half-dozen different places. I didn't even finish the thing, I just shrugged and went "well, matches what people have told me, no new info here".
The first time I was warned away from Amazon, it was over specific (and probably unenforceable) pieces of their internship contract. A friend rejected his offer because it contained a bizarrely broad non-compete that could theoretically have barred him from ever starting a company with anyone else who had ever worked at Amazon. This was 2012.
The second time was from a friend-of-a-friend who spent one year as an SDE. He talked about bureaucracy, burnout, and made the Microsoft comparison. He said it Amazon was reasonable as a ~2 year cash out, but nothing more. This was 2013.
After that, I was still open enough to respond when I heard from a recruiter. The internship interview required invasive rules like the ones at issue here, which proved fundamentally incompatible with my machine/internet setup at the time. I declined it, and scratched off Amazon unless I got news that these things had improved. This was 2014.
How you deal with mistakes is what counts, agreed, but Amazon's reputation struggle is far older and more pervasive than the perception spread by the NYT story. Fair or not (and I honestly don't know), it's a long-standing issue.