Apparently there are a lot of people confused about this, but no, Amazon does not have ownership over the Washington Post. Jeff Bezos bought it with his own personal funds using an LLC: https://en.wikipedia.org/wiki/Jeff_Bezos#The_Washington_Post
And surely there is no relation between Bezos and Amazon so the part about "This is what we get allowing mega-corporations control our media" is obviously false.
The distinction is not wholly useless, since it provides a frame whereby we can interpret this as evidence that the corporate veil is fictive, and that the "evil corporation" problem is actually caused by evil individuals.
My instinct is that Evil Man theory is as simplistic (and wrong) as Great Man theory: there's probably some better explanation that this also provides evidence for, that I'm missing.
I think people struggle with the fact that it's not a legally so. However, per the article, Bezos is exerting power over WP because Amazon lost contracts to Microsoft (due to WP being critical of Trump). Their balance sheets may not be aligned, but their interests are.
And if Bezos toes the line and does things that Trump likes, then Amazon may benefit.
Trump sees "friends" and "enemies" [0], and doesn't care about actual ownership of shares. "Bezos is a friend and sorted out that WaPo mess, so I'll cut him some slack and kill off that Amazon anti-trust thing" is something we can all picture Trump saying.
[0] Obviously I have no idea what he actually sees or thinks, but this picture seems to match his public pronouncements.