Mr. Snowden said he could read any citizen, even the presidents, email if he new the address[1]. Theres a number of ways this could be accomplished, hopefully the technically details of which will come out eventually, but theres no question he saying its being accomplished.
However there is a question of how much exaggeration he is using.
For example, technically a police officer could shoot anyone if they wish. The only thing stopping them is society's laws.
That the NSA has the capability to ask any company for an email address's data is different from any employee having the ability to do that peeking without repercussions.
http://www.guardian.co.uk/world/video/2013/jun/09/nsa-whistl...