In an interview with the Guardian he said, as you quote
"Nothing's been done about that story, it's one big lie, not one word of it is true".
You take this statement he made and translate it to "his claim that the US never killed Osama bin Laden". The original quote you print is much clearer. I certainly don't translate his quote to what you translated it to.
Speaking of changed claims, both the White House and New York Times walked back claims they made in 2011 about bin Laden. So Hersh's claim of "a lie" and "not true", if you want to call it that, is true by their own admissions.
Incidentally the disputed issues are did anyone high up in the Pakistani government know bin Laden was there, how did the US learn he was there (connected to the first point), was the firefight killing bin Laden a kind of John Wayne/Audie Murphy production or was it more pedestrian etc.
If it's not pedantic that Hersh telling the interviewer "not one word of it is true" was hyperbole, when at least one word of the White House story was true, then you have a point on that statement. But it still does not automatically translate as you said. The original statement is more clearly what he said.