I have walked across the border to Boquillas. There is nothing there except a few adobe huts and some burros. The river is very shallow. No bridge. Boquillas is a dusty little nothing town. I am not even sure you can access it from Mexico. It is at the bottom of Boquillas Canyon, on the Mexican side.
I've been down there to where that crossing several times. There's always some guy selling walking sticks or copper wire scorpions or something, but since 9-11 they stay on their side for the most part. I'd have no problem with a crossing there, it is a very remote area and not likely to be a huge crowd going either way. I think the illegals come in farther out west for the most part, through the ranch land and not so much in the National Park. But there are roads down to Boquillas, at least one. I've sat in the desert at night and watched headlights way down to the south, moving toward the Boquillas area.
I understand people's objection to this but that area is pretty well patrolled and watched. If it comes to the point there are trucks full of people coming across the river there (and you can drive across in at least a few places) then that would have to be stopped.