If Twilio's overall service wasn't excellent, people wouldn't be nearly as willing to view this from the positive angle. If Twilio weren't a startup - if it were, say, SalesForce.com - this also would hurt more than it would help.
Fortunately, Twilio seems to know this. They're absolutely in no way resting on their existing positive reputation. Even though they've earned the trust and respect of so many customers, they're still treating each and every customer as if they must still continue to earn their trust and respect.
Word of advice to Twilio execs: when this is all done and over with give your PR people a bonus and/or a raise. They did a fantastic job here in a nearly impossible situation, and I'm sure the recruiters are circling like sharks.