It would seem the adjusted basis on your supplemental information page is accounting for the increased basis that was included in your taxable income (the funds you were taxed on when you exercised your options). This should be accounted for in your tax basis (cost basis) of the stock.
If the figures make sense based on that theory you definitely need to adjust the cost basis in TurboTax to reflect the accurate gain. You should compare your taxable wages with your supplemental sheet to make your determination.