I don't know, I really do not see an issue with the job. You are basically a "First Responder" to meet OSHA's on site First Aid requirements. I was an HSE specialist for many years as a dual role I had for an overseas federal contractor. Now being the ONLY paramedic on a remote FOB and being the HSE Coordinator, that was a direct conflict of interest. LOL And if you know OSHA rules and what constitutes a recordable versus a non-recordable and how those labels impact companies on existing and future contracts, your actions or inactions can literally cost millions.
As for this role, how you have described it thus far, I do not have any alarm bells going on myself. I am sure they are ringing for you or others who have possibly not done many industrial OSHA type jobs or are relying on the lawsuit/liability mantras which are hammered so hard through school. I mean it is a real thing, not dismissing that, however it seems to be more of a boogeyman than what it truly is.
As for the meds, these are all OTC meds. If these people were at home, what would they do? They get a headache, they go to their medicine cabinet and they chug some pills. They are adults and at work. They get a headache, oops they do not regularly carry tylenol, and they do not want to go home. They just want a pill and to keep working. Give them a dang pill. They do not need physical exam, vitals, etc. They are not "patients" in the context we normally see patients in. They ate a sausage biscuit from a questionable gas station on the way in to wok, now they got the poops...give them some Imodium. Back to work. One standby company I worked for many moons ago (for anyone who wants to argue the above about this being "prescribing meds"), we simply had a large tackle box filled with OTC meds. We pointed at the box, said help yourself and left it at that. You know, treat people like adults.
I am on the fence, if the pay, the hours, and the benefits work for you...give it a go. IN time you may be able to effect some change. Right now, run with how it is and make the best of it. If the pay, hours or benes are not that good and you cannot sleep at night anguishing over this...then bail.