He was an IT administrator who had Sudo access to pretty much everything. I’d be careful of a lot of the stuff you read in 2013. There was and still is a concerted effort to discredit Snowden and make people feel he is a traitor.
Example: why did they cancel his passport after his plane left for Russia? (To say he’s a Russian spy)
There’s a lot of examples of this. Highly recommend some of the documentaries on the subject I and some recent discussion on the topic.
Snowden gained the vast majority of the electronic information from scraping web tools he had access to. Recall the "wget hacking tool" controversy, where he used the command line to retrieve internal websites. The removal of that information, and obviously the disclosure of it, was illegal.
The government didn't present a release claiming a substantial portion of the information was retrieved with that password list.
Snowden convinced colleagues to give him their passwords: https://www.theatlantic.com/national/archive/2013/11/snowden...
A Google query for "Snowden stole passwords" returns a lot of results.