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Some useful links can help you. Don't know have you read these kb articles or not.
You can achieve this thing by doing the following steps:
1. Assign the site role to the user as Interactor. Due to this, he won't be able to publish.
2. Assign the permission to that particular user at workbook-level and the view-level as "interactor" or the "Editor"
Through this, when he logs in, he can web edit the permitted workbooks/views but won't be able to publish any!
Hope this helps Rohit!