The historical Russian counterpart to NATO was the Warsaw Pact, which was pretty clearly solely an instrument by which the USSR exerted its will over its member

The historical Russian counterpart to NATO was the Warsaw Pact, which was pretty clearly solely an instrument by which the USSR exerted its will over its members --its primary intervention was to invade a country that wanted to leave. So it's not entirely unreasonable for a Russian to look at the NATO as potentially acting like the Warsaw Pact did, although, as you note, the fact that much of NATO doesn't share the same foreign policy as the US (indeed, often criticizes the US's foreign policy aims!) should disabuse them of that notion.