Privacy laws don't really apply to employment verification. Many US employers are reluctant to give a bad reference, because they fear they will be sued. Other companies have a policy that they give only neutral references, or only verify dates of employment (and possibly salary and/or rehire eligibility.) The only information they are LEGALLY prohibited from sharing would be your medical history.
The employer generally can reveal, without liability, anything factual about your record: "Pat was fired", "Pat had three unexcused absences in the last month here." "Pat failed an apprenticeship final exam twice". If you don't want a bad record revealed, don't compile a bad record.