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You can replace DataSubmissionService by your own, and override the method GetSubmissionData where you could get the base data return then remove the field SubmitUser. That will prevent saving user information to storage.
Is it possible to remove user information from the form submissions tab when posting forms from for instance an intranet were the user is logged on to the system? I know about the default checkboxes but this does not remove the user information when posting a form as a logged in users. Any suggestions?