I've had this happen on 3 systems, 2 of them set up nearly the same and 1 set up pretty differently, so I think it's probably repeatable. When I use the module with more than one Node Reference CCK fields, the links (in my case Edit and Add New) don't show up depending on the user's permissions.

The easiest demo for testing is a "container" page that has 2 Node Reference CCK fields (just in order on the container page, say Node#1 and Node#2). When the user has node_access('update') permissions for the Container and Node#1 but not Node#2, the Edit, etc Admin hover links show up. When Node#1 and Node#2 are switched, then the Edit links don't show up for any of the nodes. Switching back (or to other node references with the same permissions) and the hover links show up again.

I've tried it with a few more Node References and as long as one that the user cannot 'update' is ordered before one the user can 'update', then none of the hover icons appear.

I suspect it's the Javascript that isn't writing the

tags, but I don't know enough to test that out.