This is, in my opinion, an overly straightforward conception of influence. I'm not saying Bezos would want to buy the Washington Post in order to effect positive coverage of Amazon.
Calling people and starting a PAC with a transparent agenda is not nearly as powerful as controlling one of the few trusted, prestigious political news outlets left. You can influence operations without directly interfering in the newsroom, and you can do so while appearing to give the paper autonomy. The fact that flagrant, visible abuse would be self-defeating doesn't really tell us anything.
I guess I'd ask this: if the newspaper is not valuable for its influence, why buy it at all? It will not make him money, he is not bored. Even if he is buying it to keep it out of other hands, that remains an agenda and an active use of influence.
