Funky permissions won't let weblinks be viewed by authenticated user unless they are given edit permissions

I must confess I'm not real clear about how the permissions work on Drupal, but here's my problem. We have entered about 200 weblinks that can't be viewed by users who don't have edit permissions. The nodes won't show up, and they aren't listed by sitemenu or site_map. We are using node_access_by_role and that generally seems to work, except that the function doesn't show up in weblinks nodes.

Any ideas where I might start to try to figure out the problem?