If you have added dropbox to the Acrobat application then it will open the dropbox files with out asking for password. This facility is provided for your ease to view files.
Please let us know if you have a different issue.
My point is that Acrobat creates an unprotected route to items stored in my dropbox.
These items have been stored with a password protection in dropbox deliberately so that if my mac was stolen or lost, they could not be accessed by a third party.
Acrobat reader is therefore a security risk on ipad and other mobiles.