Yes, the Russians believe. His approval rating since the begging of the operation increased significantly.
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Putin isn't Sauron, and the Russians are not Orks. A single person can't block all his people from the truth, especially in the age of internet.
You say, that NATO is a defensive alliance, but the Russians did see operations in Serbia, in Iraq, in Libya, in Syria, etc... You sorry, that the Ukraine "was not admitted to NATO", but from their point of view - you sorry, that Russia finished genocide of the Russians in Donbass, and they get pretty good reasons to consider you as a direct threat to their lives, or even as an actual enemy.
If your position (however sincere) is "You guys are blind morons, controlled by an evil super-monster, and we are valiant knights in shining armour, who never attacked another state" - they won't take it seriously. Actually they take it as an insult.