Having some document in hand is a plus. Having it in Russian would be better but the mystery of the English/Turkmeni might add to the feel of international officialness to it. Is there a stamp on it? A signature? Those are often appreciated in that part of the world as well.

Per law, or at least our collective understanding and experience with it, you should be ok here. I do hope you'll report back and let us know how it went. Hopefully, this will be a non-issue on what sounds like otherwise a pretty interesting trip. All the best!