It may be that a more subtle person would find for this thing a reason of greater subtlety: but such is the reason that I find, and that liketh me best.
Migrants come up and no longer seek to evade the Border Patrol, but are actually left at the border by their smugglers. And they seek out Border Patrol agents or Customs and Border Protection officials to surrender to them and request political asylum. That's the way in which they get entry into a system that will eventually release them into the country.