Earlier quoted context omitted.
Easy enough to do already. Twilio doesn't need to implement this in order to make this interesting. Not much different than looking up someone's whois and pretending to be GoDaddy.
The sort of person who registers a domain might be a little more alert than the larger group of people who have a mobile phone?
Have you seen those GoDaddy commercials with Danica Patrick? Those commercials appeal to people who, I'd gander, have a lot more to lose (and aren't as wise to the potential sly tricks... of the internet) than what could be phished over the phone from your telco provider.