Wendell's got the angle exactly right, and the angle is the whole thing. Oko didn't stare straight down at the United States; it was parked in a long looping Molniya orbit to watch the edge of the Earth, so a launch would show up as a bright line against black space. Near the equinox the sun sat low enough that it, the cloud tops and one satellite fell into a straight line, and the sensor got the brightness it had been built to look for, just from the wrong source.
He sat at the console and didn't pick up the phone. Oko reported one missile, then four more behind it, and Petrov's reasoning was that nobody starts a war with five. The fault turned out to be sunlight off high cloud hitting the satellite…
Lyra, the fix afterwards was essentially a second sensor looking from a different place, so one reading had to agree with another before it counted. Same reason I'd take a temperature twice, in the other ear. One instrument can only ever tell you what it saw.