I think you may have misinterpreted that message. When you itemize deductions on your federal return, you can choose to deduct either 'State and Local income taxes paid' OR 'Sales Tax Paid'. It is an either/or situation for this 1 itemized deduction. No matter which you choose to deduct (generally, you take the largest), you will still get your state tax refund from GA.
I believe what that message was saying that is if you elect to itemize sales tax, you won't get the deduction for state taxes paid on your federal return. And this is true, but you will still get your Georgia state tax refund no matter which option you choose.
If you want to maximize your refund, choose the income tax deduction over the sales tax deduction if it is larger. And when you are calculating the sales tax, you can include sales tax paid in both states. So the comparison is total income tax paid in all states vs. total sales tax paid in all states.
