Problem with Node module on website
There are a number of permissions that could be affecting this.

First off, node permissions.  The most important one here is 'access content,' so make sure anonymous users can do that. After that, they can be set up so different users in different roles can create, delete and/or edit nodes.

Given that they aren't trying to do any of this, I doubt it's related to these node permissions, so let's go drill down a granularity level and look at permissions on fields in the nodes themselves.  Here, permissions can be set on edit and view.  Given they aren't trying to edit a node, just look at it, I'd look at the view permissions. 

Assuming 'admin' is uid 1, s/he can do anything, so look for fields that aren't viewable by the more casual user/role.  Somewhere in there as you surmised above is the field that this module needs to show itself.  (Oh, also, if you are using imagecache, make sure its permissions are set up as well)