It's the same with most "Island" draw tags. Pretty much all private property and no public access. I have secured some private property to hunt here on Whidbey Island where I live, and got drawn for a second deer tag this year. I wouldn't have put in for it, without the access to private land. Even though there is still some small tracts of public land to hunt on Whidbey.
You're not the first to get drawn (even by "accident") for an Island tag, and then find out there really isn't any public land to hunt. Sucks, but it happens.

Gary