I doubt that diabetic or high blood pressure medication would be a touchy issue. But it almost certainly would be for narcotic painkillers, where the risk of abuse or criminal activity is well known.

If you didn't have a regular physician, you might need to work up to an emergency stash. For example, if you can show him/her the unused prescription, or the full bottle, after 30 or 60 days, you will hopefully build up a degree of credibility and trust.