Can we (the government) make it mandatory for the contractor to tell us why they fired, moved, relocated, or why contractor employees left the existing contract or government? Isn't that kind of information of the contractor employee protected somehow??
This answer is provided based on the facts of the situation as present in the question. We recommend you get contracting officer and legal advice as appropriate.
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The contractor-employee relationship is a contract, one the government does not have privity to (much the same as a prime-sub relationship). Your answer to the administrative assistant was correct.
If the government had a (substantiated) reason to believe these actions had to do with the performance of the contract or some other government interest, e.g. security or a criminal activity, then the contracting officer could reasonably make inquiries.