The argument is not that the color index is a perfect replica of GDP, but that it is an independent, higher-frequency proxy for economic activity that captures dimensions missed by traditional reconstructions.
The value of the index lies precisely where it converges with broad historical trends and where it diverges, suggesting new information. The observation that the color index frequently changes before GDP is a sign of its validity, not a weakness - e.g. shifting consumer demand/sentiment or supply chain shocks and a leading indicator of GDP