I received paper statements too.

The reason is a legal one. You should notice that the new details about late payment charges and that sort of thing are printed on them. American Express told me that they are legally bound to ensure that they inform all members as it is a change to the Terms and Conditions. The notice on the statement is in addition to the letters they sent out a few weeks ago. They apparently have many account holders who do not read online statements, so must use the post!