A password is asked although Adobe opens the document without one when the document is encrypted with "Encryption of data using the RC4 or AES algorithms with a file encryption key length of 40 bits." - Version 1 (V 1) Revision 2 (R 2).
Similar cases (V1 R3 and V2 R3) are handled in the following item: PdfViewer: A password is asked although Adobe opens the document without one.