To chime in here.....
As a former technician, now working for the 999 ambulance service, you've got to ask about the sensibility of people saying no all the time to basic first aid or medical problems.
If someone asks you if you have paracetamol, and you do, then offering them some is not some sort of gate to hell.
Be sensible with that you offer, IE no aspirin for pain where someone is on blood thinners, encourage them to read the leaflet if needed, but we need to step away from the doom based thought that you will be sued every time. It simply doesn't happen.
You are more likely these days to receive a bad venue review on trip advisor or similar if you DON'T provide small items like pain relief, ice packs etc.
I went to a very large holiday resort this week for a wasp sting ........ oh no, we cant possibly have piriton in our bags, that would be a drug. yes, a very safe, very effective drug, that anyone can buy over the counter. Just follow the instructions on the bottle and voila, your client will be happier. Instead, their client was very upset that the resort safety team called an ambulance, wasted their time, for something so minor.
People need to take charge of their own wellbeing again. You aren't selling them heroin, you are offering them a free pain relief tablet.