Perhaps you are confusing the two Forms 1099-R. TurboTax never asks for your basis on a distribution from an inherited IRA, it just asks for the taxable amount that you must calculate outside of TurboTax.
The distribution from the inherited IRA will have code 4 in box 7 of the Form 1099-R.
The distribution from your own IRA will have code 1, 2 or 7 in box 7.
Make sure in the questions that TurboTax asks after entering the details of the Form 1099-R that you correctly indicate which one is inherited. (For some reason TurboTax does not automatically determine that from the code in box 7.)
