Section 336's notification requirement obviates the AMA Safety Code notification requirement since 3 miles is less than 5 miles whether you are talking about statute or nautical miles. So there is no longer any need for the AMA's notification requirement since you will have already notified an airport if you are within 5 SM of it.
BTW, the FAA has clarified that they view Section 336 which, which did not say which kind of miles either as meaning SM and not NM.
Footnote #9 bottom of page 13:
9 For ease of determining distance, the FAA interprets the statute to mean 5 statute miles