I know it's fun to hate on the big tech companies recently and act like they are bullies (and indeed in many ways they are), but this is a bad example of that. Most companies I know of would outright fire you if you, against explicit company policy, went to the press and started badmouthing your employer. The fact that Amazon only gave her a warning is the only surprising thing in this article.
If your stance is that Amazon's policy regarding public speaking is wrong, then that again is your opinion. I reached out to a friend who knows about Amazon's public speaking policy. The policy does not prevent employees from speaking to the press, nor does it prevent employees from speaking negatively about Amazon. It actually even says that talking publicly about an employee's experience working at Amazon is encouraged as long as you say that "this opinion is my own and not my company's".
The policy does also say that employees must get prior approval before speaking publicly on behalf of the company or before sharing confidential information. I personally see absolutely nothing wrong with this policy, and the employee in question definitely violated that. She explicitly identifies herself as "an Amazon insider" in her interview with TechCrunch where she then goes on to talk about Amazon's effort regarding climate change.
If I had to guess, I would say that this phrase is probably what got her into trouble. No company would be happy if one of their employees, without prior approval, represented themselves as an "insider" giving special information to the press, and I don't blame the company for that or see anything wrong with enforcing policies against that (except in cases of actual whistleblowing, which this is not).