I get calls now and then from folks who are the subject of a discrimination investigation.  The best thing you can do is cooperate with the investigation.  You are still an employee and could be terminated for failing to cooperate with an investigation.  Do not expect fairness or even high quality.  There is no duty on the part of a Texas employer to conduct a "fair" investigation.  In Texas Farm Bureau Insurance Co. v. Sears, 84 S.W.23d 604 (Tex. 2002), the Texas Supreme Court refused to recognize a claim for negligent investigation of an employee’s misconduct.  A claim for negligent investigation would damage the at-will relationship, said the court. 

Indeed, the employer does not necessarily need to conduct a "quality" investigation.  In a "he said/ she said" scenario, the employer can believe anyone it chooses.  The only exception would be for someone who is a member of a union or who has an employment agreement which assures some degree of "just cause" for termination.  But these situations apply to few workers in Texas.   

An employer is required to conduct a "reasonable" investigation into allegations of harassment in regard to discrimination.  Bu, the reasonable requirement is based on its effects in stopping or curbing harassment that might violate Title VII.  The reasonable requirement is focused on the victim of the alleged harassment, not the alleged perpetrator. 

I have spoken with a few managers who were unjustly accused of discriminatory conduct.  Unfortunately, there is little remedy for such persons.  Defamation is at least a possible lawsuit.  But, defamation has an extra high burden in the workplace.  So, yes, if you want fairness at work, form a union…..