Why would the insurance company have done an appraisal?  That's like saying an attorney should do an appraisal.  (OK, the original post says that.)  

It's not clear whether the fire happened before, during or after the father's death.  I would say the FMV at date of death was the value of the restored property once the insurance company finished its work, and if it sold shortly thereafter, then there is no gain or loss except for selling expenses.  Maybe throw in the landscaping she paid for.  Not the trash hauling, that's an estate expense.  It's more difficult to make this case if the fire happened after death, but why not?  The FMV of an insured property includes potential insurance compensation.  

In some counties and parishes, the tax assessment is helpful if it can be used to compare the property to others that recently sold.  But then, how long did this restoration work take?  When property values are increasing at a 20% annual rate in some places, there might be some gain before selling expenses.  Unless this was a million-dollar home and the taxpayer has a million dollars of income, I wouldn't lose much sleep over it.