I know this is an old question, but since we had the same question and finally figured it out (in LTS2015), maybe this will help someone.
Are you using custom form layouts and a custom tab? If so, the tab widget containing the custom form layout has an option to "Show edit options". Set that to "No".
Are you using the Document Edit Layout? If so, navigate to Documents -> your document type -> Tabs -> Default Tabs Filtering and check "Comments" to disable it. (or Definition -> Document Facets -> uncheck "Document can be commented", although this can be overridden by using custom form layouts).
