Well, it appears from their own statement, lds knowingly break immigration law in every country they are involved in.
Interesting discussion on some of these things at an ex-Mormon board this weekend. One poster cited Lds relatives of Lds missionaries blaming "Satan" for this setback. One poster then responded: So, Satan made the LDS church authorities break the law resulting in the missionaries being expelled from the country and thus hampering the work of the lard? That Satan is one tricky dude.
Another posted added: I was in VZ [Venezuela, which is near Guyana] from 2000-2002 and there were issues with our visas having illegal stamps. I didn't ask many questions, just handed my passport over to the MP like everyone else (I had never had one before, hadn't traveled before, and didn't know how dangerous that was!). Who knows what happened to the original. They just told us that our old ones have been destroyed and that we had to get new ones and take a trip to Trinidad and Tobago or Colombia to have them re-stamped. I heard rumors that the church's gov't insider had used outdated stamps to automatically update our visas and that some elders trying to go home had been detained. I was also under the impression that we were there not on missionary visas, but "educational" visas--as in student visas.