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Not sure if I am getting you here.
But just in case this is a simple mistake (due to a poor design - no ofence the module is great but this was a little short sighted)
You have to give permissions for those that can approve news items and press submit (Do not worry about the other options on that page for now)
Then you have to go back to permissions and tick the boxes for those that can submit news items and then press submit
AND then you have to go back to permissions and tick the boxes for those that can view the news items and then press submit.
It doesn't matter what order they are done in as long as you realise and remember that you have to tick the boxes and then press submit for each permission setting 1 at a time
I hope I read your post correctly and that this helps you out.
I really like the news module, but I did think that was a pretty rubbish way of assigning permissions, still once its done, its done!
Dave