http://msdn.microsoft.com/en-us/library/system.net.securityprotocoltype(v=vs.110).aspx
If you override the default which is just ssl, around these lines in these files:
Adding in something like this somewhere, either in RestSharp or the twilio-csharp thing or your app might help:
ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12;