I do not follow US Soccer as closely as I do other sports, so perhaps my ignorance is showing here. But I'm a big believer in that if you want to overachieve or make a statement in a competition where you are very clearly at a talent disadvantage, you have to be aggressive and generally do things you might not otherwise do if you were equally talented or more talented than the competition. If you show up at these kinds of tournaments and do things conventionally, then you shouldn't really be surprised when you only get results against the teams who aren't as good and get smoked by the teams who are better.
The weakest area of performance for this team was finishing in the final third, so why not do something bold and aggressive to address that? Was he afraid that starting Reyna, or playing him a lot, might cost them a game that they otherwise would win? Or did he think he had better offensive options than Reyna? If so, I don't really see why.
None of this excuses Reyna's behavior after finding out that news, which must have been pretty bad if they considered sending him home, but Berhalter has to know that you can't play "straight up" against teams who are clearly better than you and expect to win.