Assange conspired with Bradley Manning (now called Chelsea) to break into a US government computer and steal secret files. One does not need to be physically present to commit criminal hacking.
Conspired? No.
Manning stole the info on his own, then took the info to Assange—after the fact.
If Assange was a reporter for the NYT we know there would be no alleged crime here because that scenario has played out multiple times.
But, because Assange was an independent, the US is claiming he’s not a journalist and thus not covered by the first amendment.