If free migration is a human right, Mexico does not stop non-Mexicans from entering via its southern border, right? I think I've heard reports to the contrary.
Exactly. In fact, Mexico is to Guatemala approximately what the US is to Mexico: a much more prosperous country. And Mexico enforces its national sovereignty against Guatemalans much more forcefully than we enforce our national sovereignty against "undocumented" Mexicans.
The current sad state of affairs exists because of one of those occasional, unholy alliances between the right and the left. On the right--at least, the pro-business portion of it--are businessmen and Chamber of Commerce types who want an inexhaustable supply of cheap labor--no questions asked. On the left are the transnationalists--who, just by definition, believe in open (or better yet, nonexistent) borders; and those who believe that the current world order is unjust, and must be upset by any means necessary.
The anarchic mindset of some invaders (and that is what they are) can be seen clearly in their cherished motto: "We didn't cross the border. The border crossed us."