I can't see a downside to sealing meds in an airtight, opaque container (bag or otherwise). I would however be aware of temperature extremes in storage. If your kit is in the trunk of your car, I would assume that heat will degrade your meds pretty quickly, so rotate them out on an increased schedule. As to prescription meds, my thinking is that in a disaster scenario, cops aren't going to quibble over my blood pressure pills. If I'm in a routine traffic stop, and they want to empty out my G.B.H.B. on the roadside, I'm already inconvenienced to the point that having them prove that the prescriptions might not be mine, could be entertaining. I would think that the firearms I carry (legally and licensed) would be of more interest. I do agree that having copies of the prescriptions, along with the meds might not be a bad idea (I should probably start doing this).
As to the Zip-Loc of aspirin, I have a friend who brushes his teeth with baking soda. He was pulled over for a taillight and had a bag of baking soda on the seat, along with some other stuff. Needless to say, he got a trip to the cop-shop. Maybe not quite so entertaining.