If they found a link, they found a link
You could have skipped the wall of text. They didn’t find a link. They found a random correlation.
The scientists here essentially engaged in P-hacking: https://en.wikipedia.org/wiki/Data_dredging
Munroe didn’t misunderstand the independence of the experiments at all. He understands that misleading spurious results can arise from repeated experiments.
And it needs further research. Not less, not more.
No it doesn’t. At least not anymore than the other colors. A positive result is no more deserving of further investigation than a negative result. What you are describing is bad science.