I think the point for some would be that it's risky to mix whatever med she was taking with alcohol, especially while children were dependent on her for their care and protection, especially if they were taken at the same time or close together. Anxiety meds might be just as dangerous in that regard as a narcotic.
I don't look at much about this case outside news articles and our forum here, so I didn't know there were rampant drug addiction rumors. She might've been better off just to have said she takes prescribed medicine in prescribed doses at appropriate times. Emphasizing it wasn't a narcotic doesn't really dispel an addiction rumor since narcotics aren't the only meds people get addicted to.
She mentioned the same thing about her med not being a narcotic in her MK interview. Were there already a lot of people accusing her of being a drug addict that early on (if you know)? Thanks.