I think technically the problem wasn't that the US had cancelled his travel documents, as the Ecuadorian government could grant the necessary document to a refugee (which is almost what happened[0]), but rather that he was worried the US would force his plane to land in a country where he could be arrested.

That fear was well-founded, given what later happened to Bolivian president Evo Morales when the US suspected he might be transporting Snowden out of Russia[1], even though forcing planes to land to capture political prisoners is more fitting for a dictatorship than a democracy[2], but I suspect that Russia made it a condition of Snowden's safety that he not attempt to travel to any other country.

Of course I'm not saying I would have done anything differently were I in Snowden's position, but it is worth noting that he could in principle have avoided US and NATO airspace by travelling from Russia to Shenzhen to Johannesburg[3] to São Paulo[4] to Ecuador.

[0] https://www.democracynow.org/2019/9/30/how_edward_snowden_av...

[1] https://en.wikipedia.org/wiki/Evo_Morales_grounding_incident

[2] https://en.wikipedia.org/wiki/Ryanair_Flight_4978

[3] https://www.flightconnections.com/flights-from-szx-to-jnb

[4] https://www.flightconnections.com/flights-from-jnb-to-gru