Is it possible to grant users or security groups other than Admin or Host the ability to upload files?

I have given users edit permissions and created a new security group with full edit access to many pages. In File Manager they are able to go through the process of selecting a file and they see the Upload button, but when they hit "upload" it doesn't do anything. No file is uploaded and it just goes back to the file manager and seemingly just aborts the process. Admin or Host accounts do the same thing, but the file actually uploads.

In DNN5 this was not a problem. Wondering of this is still possible without being an Admin or Host?

Essentially, I want to avoid having to get admin involved when a user wants to post a large file on the website.  (I'm using version 7.0.5.)  I came up with the following cumbersome process in which non-admin users have viewing rights to the File Manager.

Our users can upload large files using FTP.  However, in order for an FTP-uploaded file to display in dropdown selection list, someone has to view (not sync, just view) the folder to which the file was uploaded.  Even though File Manager is meant for admin/host users only, I followed Brian's lead and granted those users permission to view the folder in File Manager.  They are then able to add the document via the dropdown list in a module.  Is there a better way of doing this?

The best approach would be a simple custom module based on the DNN File Picker control - if you have some c# skills it would be a very straight forward module to create.
I assume the users are uploading to their own user folder in this case ?