They probably don't have access to the report object structure(s) for the application. If you don't have access to a report object structure, the only content you can select is from the base table so the only type of report you can build is a list report. If you switch to the content tab you should be able to tell if they have access to any object structure.
I assume a valid report object structure exists since there are out of the box object structures for inventory. To grant access to their security group(s), in the Report Administration application use the Set Report Object Structure Security action. This will open a dialog for you to add the additional group(s).
