For what it's worth, my amateur interpretation is this:

- It was a Soviet satellite whose trajectory wasn't recorded;
- The US Air Force recovered it, but let the meteor story out as a cover;
- The US Air Force gave parts to NASA to examine;
- 40 years down the track there's no need for secrecy, so NASA reveals what it had previously kept secret.

The main challenge to this would be the accuracy of information about Soviet satellites. For example, what sort of record would there be of the satellite if it re-entered the Earth's atmosphere on its first orbit? Is it possible for a spacecraft launched from the USSR to follow any of the claimed paths?