Employment labor Texas law, employers disclose of employee issues, employment references

If I'm reading the question right, it looks like this might be regarding references given by the employer. Employers can give references about employees, even if those references are negative. An employer is open to liability, however, where the reference given is untruthful and is given in bad faith - where this is the case, the employer might be successfully sued for defamation. Proving defamation can be difficult, however.

An employer is exposed to civil liability when the reference given is untruthful. I agree with Ms. Weil's fine observations.

In addition to the prior answers, there may be a common law (not from a statute, but from caselaw developed over the years/centuries) claim of invasion of privacy under Texas law. If there is any authorization that you've given for disclosure, the employer/supervisors have been given "carte blanche" from the Texas Supreme Court, which is pro-business and tough on employee rights (there have been 9 Republicans, all from business/employer-friendly backgrounds, on the Texas Supreme Court for many years), so the burden of getting past the tough defenses to defamation and invasion of privacy claims are extremely high, especially if the employee has signed any authorization as part of the hiring process, or at a later date related to a job search.