Just to clarify, any visitor to Belize can go into the Free Zone at the Corozal border. BUT you have to go through immigration and pay your US$18.75 exit fee. From there, you can a) go to the casinos which are near but not in the Free Zone -- Princess, Royal Princess and the soon-to-open Las Vegas b) go into the Free Zone and buy gas or whatever, or c) go on into Mexico.
Visitors do have to surrender their passport at the Free Zone gate, but they get it back when they leave.
In fact, the whole thing has a logic that escapes me. The casinos, for example, can be visited by Belizeans or permanent residents who don't have to pay the exit fee, and by Mexicans, but not by tourists in Belize unless they pay the $18.75 exit fee every time they go.
There's really not very much of interest in the Free Zone, unless you're in to cheap Chinese clothes and household gee gaws ... or fuel. A couple of weeks ago, I think I paid about Us$2.75 a gallon for diesel there (prices are by the liter), a savings of 75 cents or so a gallon from the Belizean price, but not a huge amount. You'd save more on gas.