I make the effort to learn things from topics here by following the referenced link and look at the situation for myself. If you prefer to be spoon-fed your thoughts, that's on you.
The OP's referenced link made it quite easy to see the situation county-by-county throughout the nation. When I looked at the map I saw Dukes County was indeed higher than most other surrounding counties, but was nowhere as bad as the situation on nearby Nantucket.
I suspect that Martha's Vineyard rate is very much higher than the county-wide figure. It wouldn't surprise me if it was similar to Nantucket's and thus I believe there's a broader explanation than Obama's birthday party. I question why these islands would be similar to what's apparent in the South?