You could not create a new Twitter account with out a phone number last week. (Attempting from US). It rejected my disposal number as invalid too. :(
When opening a support ticket about it, they claim it was a "mistake and" offer to unlock the account but I always suspected it was a disgusting tactic for harvesting phone numbers and I guess I was right.
I know there is Google Voice, but it I don't want my disposal number to be linked with my real phone number.