The saying is of course an exaggeration but the Mongol Yam as it was called was very effective. Yam was a system of stations set up across the empire. At these stations bearers of a particular passport could acquire food, water and fresh horses. Up until the reign of Mongke Khan the Yam was completely free to use for merchants. The Mongol empire understood the value of trade and the use of the Yam system along with the informal Yasa code of law produced such a surge in trade that major trade along the silk road reopened after almost a thousand years of dormancy. This along with other benign aspects of the Mongol Empire such as cultural and scientific exchange has been called the Pax Mongolica by modern historians. To answer your question I do not have any specific knowledge on the security system in place for the Yam but I can tell you that it was safe enough that trade flourished to the extent that the Mongke Khan had to tone it down by implementing taxes on merchants.

Most of this comes from Genghis Khan and the Making of the Modern World by Jack Weatherford. One of the more biased sources but it contains good information none the less.