Huh? Why Bayesian is better I don't understand

So it seems Ziliak and McCloskey are getting a lot of attention at the moment, as they've published a new book.  Tim Harford blogged about them, and now there's an article in Science News about them.

I suppose I should really be pleased that scepticism about statistical testing is getting a more widespread audience.  There's little doubt a lot of dubious stuff is done, especially in economics by people wedded to their theories.

But there's something very off-putting about the virulence of Ziliak and McCloskey.  They are no better than the academics they criticise for taking some argument/rule, and pushing it fundamentally.  If you have a moment I'll leave you to their responses to critiques from two of the finest minds in doing statistics properly, Aris Spanos and Kevin Hoover (Google link).  They also don't refrain from taking a pop at Clive Granger because he dares not to fully agree with them.  If anyone disagrees with them, it's the other guys that are misunderstood, it's not that Ziliak or McCloskey could ever need to learn anything new - they've already cornered the entire field, and made sense of all the mistakes the rest of us have ever made.

But anyhow, the Science News article puzzles me.  It goes the whole length talking about how statistics are being manipulated and this reduces their credibility, then finally says: The way forward is Bayesian!  Why is that?  Because Bayesians also use priors.  Now, priors are our prior hypotheses about the thing we're investigating.  We warp the statistical results by our prior belief about what something should look like.

Isn't that manipulation?????