This happened to me when I was working for a newspaper a few years ago. I was out covering the Minuteman thing (the original one in Naco, Arizona), and one of our stories was to head up this dirt "road" that paralleled the fence for a bit.

We got stopped by a BP guy in a Jeep, who just wanted to know what we were doing driving a brand new rental Jeep on this "road." Told him, he gave us some water, told us where the killer bee nests were and we were out of there. Aside from the USBP Drug Dog & Handler that decided to dart in front of my car at a checkpoint, I've found the BP folks to be pretty reasonable. Maybe it's because I'm white and always have the Rolling Stones or AC/DC on in my car when I roll through the checkpoint.