The FAA doesn't have much in the way of security requirements for airports, that is TSA. The only FAA regulation for airports is FAR Part 139, and only applies to certificated commercial airports like the one I work at. If the FAA is funding a fence, 9 times out of 10 it is for wildlife control. Even then, there has to be a documented need through actual wildlife strikes and/or an official wildlife assessment.
Besides, fences only keep out honest people. From security standpoint, a fence is only a layer, and one that is easily breached. You need continuous monitoring to ensure any type of real security. Even then that doesn't always work. JFK made headlines a few years ago. A jet skier broke down near their perimeter fence and floated ashore. He managed to climb their fence, walk across a mile of open airfield, and approach a gate agent working a flight and was never detected by JFK's multi-million dollar security system which consisted of hundreds of cameras and motion sensors around the perimeter.