IIRC, from the Ted Cruz citizenship debates a year ago, for a legal renunciation of US citizenship to take place it has to be before proper authority.
So, the letter describes Bergdahl’s intent, but it will be claimed that it wasn’t a legal renunciation, so therefore, he is still a US citizen.
See info posted by MMaschin:
http://www.freerepublic.com/focus/news/3163183/posts?page=68#68
http://www.freerepublic.com/focus/news/3163183/posts?page=187#187