I have the same problem. I have a certain usergroup that can access a CMS page that has a link to an attachment. When I am logged in as administrator I can download the attachment just fine so I know the attachment is there. But when I log in as the other usergroup that can access the file I get the error "Invalid Attachment specified..."
I have verified the permission settings. Any help would be greatly appreciated. Thanks
EDIT: Ok, so I figured out my problem. I had added the attachment to a forum that my usergroup
couldn't access and then used that URL for the attachment to the link on my CMS page. When I went in and posted the attachment in a thread my usergroup
could access and then used that URL for the attachment, the link it worked just fine. As usual, user operated error

Hope this helps anyone with a similar problem though.