I've never heard of any situation in which you need a visa of any kind to fly over a country. You would only potentially need one if the flight was planning to land in Russia, in which case it would depend on your precise itinerary, citizenship, whether you needed to leave the transit area, etc.
Imagine the confusion if you had to apply for transit visas for every country you overflew - on a long flight there could be dozens. The international community is sensible enough not to demand that.
In theory, if your airline provided the passenger manifest to Russia before the flight, and the Russian authorities saw your name and decided they did not want you flying over their country, then they could refuse permission for the flight to enter their airspace with you on board. In that case the airline would most likely just refuse to let you board at all, so that they could fly over Russia as planned. But this is improbable; and if it did happen, having a visa wouldn't help.
If for some reason, your flight makes an unscheduled landing in Russia due to an emergency or other unexpected event, you'd either be kept on the plane, let off the plane but kept in a closed area like the airport lounge, or issued an emergency visa. You still wouldn't need to have applied for a transit visa in advance.