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filefield_edit_access() and filefield_view_access() should use content_access() instead of checking content_permissions specific permissions. Attached is a patch that makes this change.
content_access() invokes hook_field_access() which is how the content_permissions module does its magic. I enabled content_permissions and did a bunch of tests to make sure its permissions are still enforced with my new patch. Everything worked fine! So, no one who used content_permissions should notice any changes.
However, if (like in our application) you use a custom hook_field_access() to control access to a field, it will now start working with filefield.
Of course, since this is security related, it would be really good if others could test this a bunch too in case I missed something.