I heard that my employee can now disparage the company - is that really true?

Yes - to a certain extent.  The National Labor Relations Board (NLRB) recently issued a critical decision and related guidance holding that severance agreements for non-supervisory employees cannot contain non-disparagement clauses and can only contain limited confidentiality clauses.   The NLRB went on to hold that only non-defamation clauses are permissible.  This presents a much more restrictive standard - that is not employer-friendly.  It allows the employee to be very negative about the employer, so long as the employee does not maliciously lie about the employer.   Thus, any severance - and possibly similar agreements - cannot prohibit non-supervisory employees from disparaging the employer.