An American hero does not end up fleeing to a country like Russia under a leader like Putin. If Snowden had spilled the beans and then turned himself in, I'd respect him much more.
This is real life, not a crime movie; there is essentially no value in making himself a martyr more than he already did - you're forgetting that he had to leave his family and certain future, for starters.
"American" hero is a very fuzzy concept, especially after his revelations. If the american administration has influence/power over most of the countries in the world, and now also intrusion in their communications, there's little to no place where to hide aside the enemy.