1) You are in imminent danger of being "shot in the face" or similarly harmed;
2) Your best means of salvation from (1) is communication via Twitter DM;
3) The absence of a means in which your message could be encrypted on the client side beyond the HTTPS connection to Twitter's servers would significantly increase the chance of (1).
This is a serious question.
2) environments where "your survival depends on efficiently communicating and organising" tend to ignore habeus corpus and standards of evidence. Realistically, your survival depends on external factors (your side winning) rather than hoping you and everyone you've been communicating with can withstand torture indefinitely.
2b) digitally signing a message reduces plausible deniability
Ofcourse it'd be great if twitter did the job for you, but I don't necessarily see why it ought to be Twitters position to fulfill this edge case rather than say a protester who knows they are about to go into a life threatening scenario and need to organize--both beforehand and during the escapade.