First of all, there is no law that I am aware of which requires an employer to provide a confidential complaint method to higher headquarters. Yet many employers do provide a method that allows their employees to make complaints that are confidential. Such an internal "right" will be, or should be, mentioned to every employee via a policy handbook or postings at the job site. Therefore, unless your employer has such a policy in force, your supervisor's questions are not unlawful.
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Mark B. Replogle