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Then finding out what the documented "diagnosis" was would be useful.

The correct way to answer the question does not depend upon knowing their verification process. The correct way to answer the question must focus on being accurate. Falsifying the application is a crime in and of itself.

In this case, your eligibility is determined by whether your treatment was inpatient/residential and on your doctor's diagnosis.

GC §411.172 (e) The following constitutes evidence that a person has a psychiatric
disorder or condition described by Subsection (d)(1):
(3) inpatient or residential substance abuse treatment in the preceding
five-year period;
(4) diagnosis in the preceding five-year period by a licensed physician
that the person is dependent on alcohol, a controlled substance,
or a similar substance; or

Note, if your diagnosis for treatment said it was due to dependency on pain pills, it becomes a non-issue at your 5 year anniversary.