Yes, I think the problem is with Dropbox and its default text assumptions.

I'm finding that Safari is immediately able to correctly view the freshly written file in a Dropbox folder, without any need for transformative saving. (As long as Safari's default text encoding is UTF-8)

Viewed through the Dropbox web interface, however, even in Safari, you need to manually choose View > Text Encoding > Unicode before it is correctly displayed. They seem to be serving up the text with a different default assumption, and perhaps that culture/policy is replicated in their iOS app.