Under Michigan law, CURRENT employees are allowed to VIEW their file. Nothing in the law requires an employer in Michigan to give you a copy of the file.
My summary did not specify whether or not terminated employees share the same right to view their file. Going by how other states are handled, I strongly suspect that since they did not specifically state that terminated employees can also view their file, that means either that no such right exists or at best, that the law is silent on the issue.
Unless the law specifically gives a terminated employee the right to see their file, then yes, the HR department most certainly can prevent you from seeing it. In the absence of a law guaranteeing you that right, company policy prevails.
You may want to check with the MI DOL as to whether or not terminated employees have a LEGAL right to see their file.