WaPo has publicized quite a few articles critical of Jeff Bezos and Amazon, even after WaPo was acquired. So this is something that seems to be just another baseless "jeff bad" take.
Luckily, we don't need to wonder, because WaPo has actually posted that kind of an article just yesterday, and it was extremely critical of Amazon's anti-unionization efforts [0]. The article's headline is "Amazon’s anti-union blitz stalks Alabama warehouse workers everywhere, even the bathroom". Even the headline itself wasn't sugarcoated or softened in the slightest.
0. https://www.washingtonpost.com/technology/2021/02/02/amazon-...
Bezos has no say in what can and can't be published.