As Carreyrou reports, Theranos definitely tried to pull strings with Murdoch, and apparently got nowhere with it. The WSJ timed the story to hit right before Holmes was set to appear at a major WSJ business conference.
Murdoch is a very skilled propagandist. He knew that trying to suppress this story would have backfired on him. Especially because the machines don’t work and because Walgreens would have soon learned the truth.
Nothing hurts a propagandist more than being really caught in an obvious lie. To protect his ability to slant the WSJ, Murdoch couldn’t have gotten caught suppressing this story. And he would have gotten caught if he tried.
Once the fraud was exposed and the company began winding down, spending would quickly slow down and that might have put investors in a better position to recover something, versus loosing everything.
On the other hand, it could simply be shrewd businessmanship. It's not like it was the reporting that made Theranos unviable. The tech would never work, it's just a question of time before the walls come crashing down. It's probably illegal for Murdoch to sit on this information while trying to sell his investment on to someone else (at the very least, inviting some nasty lawsuits).
Murdoch might very well have thought "Oh well, the investment is gone, I'll be damned if it isn't my newspaper to be the one to break this juicy news".
Looks to me that Murdoch acted exactly according to his long term goals.
Those guys were journos, not proprietors, but I'm pretty sure that if you could prove that a proprietor put heavy manners on the journos to do that, they would certainly be up for a criminal conspiracy charge, at least in Britain. Of course, that is typically a pretty big 'if'.