We had water damage to our engineered flooring and the insurance company has agreed to replace the whole floor because it is 15 yrs old. The installer wants to put the new flooring over the old wood. I have never heard of doing this. The insurance company said the decision is up to me to tear out the old or just leave it and put new flooring on top. Please help me make a decision!

There will be no problem laying flooring over old flooring if the standard practices are followed. There will be an elevation change so doors may need to be shortened
and reducers installed. The old floor will need to be checked for moisture content and flatness. It should need no more fasteners to hold it in place if it was installed correctly in the first place. You may need new base board or base shoe, too.
If you would like to have your home returned to the original condition, which may be stated in your policy for a casualty, you could require the old floor to be removed. This would take more time and disruption for your household.