He didn't flee to Russia. He was en-route to somewhere in South America when his passport was cancelled during a flight changeover while he was in Moscow. He couldn't fly onwards without a valid passport. IIRC, he was stuck in the Moscow airport for days until the Russians allowed him a visa.

Yep. Here ya go: He was stuck in the transit area of Moscow airport for 40 days. (Longer than I remembered.) https://www.theregister.com/2016/09/12/edward_snowden_wikile...