It's an Oliver Stone film, so it's no surprise to see a trailer that reflects the paranoid-conspiratorial strain in Stone's political views.
Stone has ideological enemies who made much of the director's historical over-reach in JFK (1991). The problem for those critics now is that Stone's wild theories about an unaccountable national-security establishment which secretly runs the country (and can even assassinate a sitting president) look slightly less fanciful in the age of XKeyscore.
Stone is a fringe figure these days, but JFK was a major success in part because it tapped into Americans' sense that the system was rigged (The X-Files was big in the early '90s too). In the age of Trump and Sanders, it is hard to argue that that feeling has diminished. Maybe Snowden is a film for the times.