Only the administrator can publish a node of content type Report. It is not using content moderation or groups though other content types are. All permissions are set for the "site admin" to create/edit own/others of this type. The only buttons available are "Save" and "Preview" and the published checkbox doesn't show for non-administrator users. Save sets as "Draft" even though it's not using content moderation.
You can use the following module.
The Override Node Options module allows permissions to be set to each field within the Authoring information and Publishing options field sets on the node form. It also allows selected field sets to be set as collapsed and / or collapsible.
This answer discusses the different permission settings that would allow non-admins to have access to this. However, that would give them too much permission that they shouldn't be allowed to have in our case (both permissions show the "Warning: Give to trusted roles only;" message). Our work around was to create a "simple workflow" that would only have draft and published states so that these users can publish.