Second: because the implication is that the New Yorker was unwilling to publish a piece that didn't fact-check out, and the London Review of Books was.
Hersh claims to have sold the story to LRB for the "politics" of it, the meaning of which is uncertain. But as he hopes to have a book published on the "war on terror", it is not out of the question that he selected them to establish rapport. And that he chose them, instead of resorting to them out of some kind of desperation owing to defects in the work itself, seems pretty clear.
[*] http://nymag.com/daily/intelligencer/2015/05/sy-hersh-bin-la...
[.] http://fpif.org/seymour-hersh-draws-even-criticism-lrb-new-y...
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The Obama administration is widely claimed by non-partisan journalists and journalist groups as being openly hostile toward the press and has used espionage provisions to prosecute officials deemed to have "leaked" inside information via the types of conversations that would previously have been considered business-as-usual. (Despite opening his presidency with rhetoric about being the most "open" and "transparent" administration in history.) This has resulted in administration staffers & officials being paralyzed and fearful of speaking with the press at all, stymieing journalists' attempts at effectively covering the government and acting as the fourth estate. While it is unfortunate that we cannot quantify whether one administration has experienced more or less scrutiny than others, blithely asserting to the contrary is not a reasonable position in this context.
[:] https://cpj.org/reports/2013/10/obama-and-the-press-us-leaks...
https://news.ycombinator.com/item?id=5701813
The most important takeaway is that the sample size on leak prosecutions is very, very low, so happenstance alone can make a President look unusually hostile. Here, it's a combination of happenstance, a shift in media norms, and cases begun under the previous President.