Mexico is a sovereign nation. The United States solving the problem is both a violation of Mexico's sovereignty and a very paternal reaction that denies the Mexican people their agency.
If my neighbor has an issue on their property, and they ask me not to intervene I will not cross onto their property to help, even if I think I should (unless you know, murder or whatever). But if my neighbor asks me to help, we should work together. It seems like we can work together in a more overt, positive, non-covert CIA way. I'm not saying this would work for certain, just that aybe we should try something new.
And regardless of responsibility for causing or solving the problem, we absolutely need to improve border security. Physical fences aren't very effective in most areas but better sensors and more human guards could do a lot to reduce smuggling and human trafficking.