I would imagine most go for a Tourist or Student visa first, that would seem the cheapest option and then just get a regular one way ticket.
Now some nationalities are good to fly into Mexico, Russians seem to go to Cancun and then fly north. Just for example and that has to be the simplest route, book a week vacation and then change your mind.
I am reminded of the Indian family the froze to death walking in from Canada, I think in that case they had sold up everything and borrowed from extended family for the trip, it was seen as an investment.
The numbers the Guardian quoted do seem high however. But then how much would be a fake marriage or E2 or EB5 etc and now is a good time.
I do not know if it is the case here but some operate on a deposit basis and you pay the balance once you get here and are working.