Many employers require drug tests as a requirement for employment. But, few employers conduct the test themselves. Most employers contract out the actual drawing of the specimen and testing. Some laboratory will perform the test. Some employers will fire an employee for testing positive for a drug test. What happens if the lab makes a mistake? Well, if the lab makes a mistake, the lab makes the mistake, not the employer. So, any legal action would lie against the lab, not the employer.
But, under Texas contract law, an employee may not have an action against the lab either. Since, the employee had no agreement with the lab. Shoot, the employee would probably not even ever see the lab. So, yes, in some situations involving a false positive, the employee is flat out of luck with no right to file suit against anyone. Not the lab and not the employer.
I get calls like this about once a year. Unfortunately, false positives happen all too often.
Same thing happens with criminal background checks. If the "checker" falsely reports back some criminal history, the employee’s action will be against the criminal background checking firm, not the employer. The remedies (ie, what you can sue for) will be limited. See Zepeda v. Industrial Site Services, Inc., 2008 WL 4822205 (Tex App. Corpus Christi unreported decision).
Welcome to "at will" employment, the rule in most states.