Think for a moment of how those deer got on the island, they swam. Which means they could leave the island the same way, so they weren't as isolated as one would think. Once exposed, the deer who stayed strickly on the island would be at a high risk of disease. Wether or not they should have been removed is a matter of debate, there is both good and bad in the decision. But the decision was made, and by folks with much more knowledge of the situation than we have.
And if anyone doesn't believe that a deer can swim that far let me assure you they can. On the river I keep my boat on it's not unusual to see deer swim across, and it's over a half mile wide there. One oyster man I know hit one in the morning fog about 6 years ago, he lassoed the buck and towed it to shore after it died.