I have discovered (after many failed calls and much testing) when Twilio SIP dials to PSTN they have been using the header "remote-party-id". This header was defined in a failed RFC : http://tools.ietf.org/html/draft-ietf-sip-privacy-00 . Although this header is supported by some SIP devices and PBXs, this was never accepted as a standard. Therfore, it should not have been used because it may cause call processing problems.
In fact, it causes certain providers to return a "Busy" and hangup incoming calls. I found out after many days of looking for the cause of failed calls. Hope Twilio quicking fixed this issue.