As you are aware, the cost basis of the home is its value at the time of the decedent’s death. Since the selling price, if obtained soon after that death, is a true indication of the home’s value, that figure is more accurate than that of an appraiser. Since you receive all of the net proceeds tax free because it is an inheritance, the other costs are not relevant to your tax situation because there is no effect on your income from the sale. You would only report the home sale if you receive a 1099-S. Since you have no tax liability for the income from the sale the realtor might not initiate that form if they understand the circumstances.
Note that this reply deals only with your situation and not any possible estate tax liability.
