It is US law, that all males, 18 and older, either legal or Illegal, must apply for the draft (Selective Service).
So while there is not a current draft, these people are not the brightest, and will believe these rumors. Add to the fact that we heard that the rumor started in Mexico, so this is there own people telling them this.
If that is the reason, then I'd suggest we draft a dozen or so and broadcast it far and wide. Talk about an exodus...