Please bring this up with someone that cares in your company: you ABSOLUTELY NEED a well working support organization with EFFICIENT escalation procedures.

Support cannot be an afterthought. If a long time customer has a critical incident like this, it needs to be caught and forwarded to the relevant people within a few hours at most. This type of PR fallout is unacceptable and completely avoidable. I, for one, will avoid Twilio just based on this story alone.