I'm running Sitefinity 8.0 and am experiencing the same permissions issue.
However I do not see User Files under the Administration dropdown in the admin. Where do I need to go to set View Document permissions in 8.0?
EDIT: I've found this:
Administration > Permissions > Libraries > View Document & View Document Library
I've set both of these to "Everyone".
However, I still cannot open the file upload links unless I'm logged into the Sitefinity admin in that browser.