Obviously Twitter does not want you to copy "their" data to Facebook. They don't get any money when you do that, and they want money. Hence, a problem.

There are several ways to get around this. Be a middleman that publishes to both Facebook and Twitter (a reverse FriendFeed). Or, sell a software product for the user to use to move his own tweets to Facebook. A user obviously owns his own content and can put it wherever he wants. A third party app, perhaps not.

(Also, why not just get tweets via whatever method the native UI gets tweets from? Do it from AWS if you are concerned about an IP ban.)