Most employment relationships are what is known as "at will". This means that a company can set the conditions of the workplace much as it sees fit. This includes requiring workers to provide proof of outside employment or school enrollment. The exceptions to this would be if such an action violates the terms of an employment contract/union agreement or constitutes some form of legally actionable discrimination/retaliation. Basically, you can either comply and supply the documents requested, complain but risk termination, or resign.