What kind of share is it? SMB? CIFS? NFS?
You should note that ThinApp does not support repositories on CIFS shares. See KB1035094.
Even though you set the Read right to 'Everyone' at the Share level, you should check at the NTFS level. As a test you can give the Read to 'Everyone' at the NTFS level but the Read permission for the View computer object should be more than enough.
If this still doesn't work, can you try typing the path with the IP address of the server instead of the DNS name.