Why do project reports say green when the real picture is different?

Because the people writing the reports are often the people responsible for the situation — and they have a strong incentive to present it as better than it is. Sometimes this is deliberate. More often it is a gradual drift: each update is slightly more optimistic than the reality, and over time the gap between the reports and the truth becomes significant. The people at the top are making decisions based on information that has been shaped by the people below them.