Just to share this Q & A since I stumbled on this issue earlier, but the most recent info dated a bit...
Context: So, I had some various "access denied" issues, following install of the "Alt-F" custom firmware, which was decent for some things but perhaps introduced this issue. In Alt-F, at a few places I did change folder user/group/permissions recursively so probably I messed this up, admitedly I ain't no expert...
But I eventually reverted back to the "official" D-Link firmware (1.05b09), so this should work if you have this firmware version installed and perhaps other versions from D-Link. I don't have any other applications installed... Then doing backups between two DNS-325 boxes, a couple of dirs and files gave access denied or some other permission issues (on either one, both boxes had Alt-F installed previously before I reverted back).
The fix: using the "My Files" application (onboard by default, no extras to install), select the folder/files producing the error, right click > Properties, then enable (check) all privileges for:
Owner
+Read +Write +Execute
User Group:
+Read +Write +Execute
Others:
+Read +Write +Execute
and then smile as the error should be gone. Just repeat until you get rid of all the access denied errors... :-)