Border Patrol was on heightened alert.
My brother and his wife were there last winter and said it got down-right uncomfortable when hiking near and along the Rio Grand. He said that there were often out-of-place people walking the trails. Many signs were posted on restrictions of buying from illegal people that would land you in very serious trouble with the USA. And of course there was opportunity to purchase. My brother recommended camping only in the main camp grounds, not isolated primative camp grounds. Hike all you like but stay on the main trails.
My other brother, older than me, he loves to camp alone. In Organ Pipe Cactus NP, another border park, he day-hiked on a designated park trail to a natural spring. While eating his lunch there, he heard wrustling in the brush, again people out of place, trying to stay out of his sight. Needless to say my brother's rest period immediately ended.
My point is.......
You need to think a little differently when camping in the border parks. Fishing at a nice quiet isolated spot along the Rio might get you into an uncomfortable situation. Camping remotely could get worse than uncomfortable. It's fine and safe to visit and stay in the parks, just sleep in camp grounds with lots of other people like yourself, doing as you are doing. Don't isolate yourself.
I hope to go back to Big Bend NP in the new few years as I have not been there since a child, but taking appropriate precaution.