When you invite a Team Member to your Pathway, you can chose to give them Edit/Publish or Published View.
Edit/Publish will allow the Team Member to work on the Task.
Published View allows the Team Member to view Data Forms and Documents which have been saved as Published Documents
When you assign a Task to a Team Member, you can decide whether they have Edit or Edit and Publish permissions
If you want to check with they have done before allowing a document to be available for Published view, you should give them "Edit" permission. If you want them to be able to save the document in "Published View", you should give them Edit and Publish permissions