So WERE their travel documents out of date? If so, why?
I'm generally very pro-LDS, but the LDS Church has willfully participated in breaking US immigration laws, so I'm not going to be quick to give them the benefit of the doubt when another country's government (however sketchy) says they're breaking that country's immigration laws.
The LDS Church could really find a much better way to handle the problem of their illegal immigrant members in the US who want to serve missions. Send them to their native countries to serve their missions, and help them apply for legal immigration to the US during the 2 years (or 1.5 for women) that they're away. If they end up having to stay in their native countries longer, so be it, but then they won't be dealing with the problem of suddenly finding themselves in a country they haven't been in since infancy or toddlerhood, and where they don't speak the language, and where they don't know anyone, because they'll already have been there for 2 years, learning the language pretty well, getting comfortable with the culture, and making social connections that can help them find employment. It would really be a very practical, humane, and LEGAL way of helping these people, many of whom were far too young when they were brought here by their parents to be held responsible for their illegal entry.
Good points GS...add the stress of knowing they are here illegally and have to be very careful not to be caught...you should send this to SLC for their consideration.