I saw Toxcatl started a study. Great!
Maybe we'll know soon whether individual skills matter. I believe so. I'm not sure how, and I can't explain counter examples.

I wish the other side of my initial question were found as by-product of this study. Do grey skills matter at all?

I have had a few 4-stars players that held well because their white skills were not far from those of a 5-stars player, so I also believe grey skills don't matter, or at least not significantly.