Wow. Interesting. We spent almost two months in far southern Arizona this year, February and March. In Organ Pipe, which we absolutely loved, we camped about 1.5 miles from the border and did some off road trails that led us to and along the border. The entire time, we saw not one illegal, no fence jumpers (there isn't even much of a fence there), no piles of trash strewn about from their run across the border, but dozens of border agents. We had a great time and loved the area. The park was open and the campground was great for a NP campgrond.
There is boondocking just north of the Park and there were quite a few people staying there. There is also some great boondocking near the Chiracahuas and down outside of Bisbee.
Beautiful area and I wouldn't hesitate to go back. In fact, we will be traveling through there again in about two weeks...