Yes it's basically legal, but you would legally be allowed to see a different doctor to get an excuse to not come in. Any employer can require a doctor's excuse when you call in sick. A lot of people call in sick for the wrong reasons so many employers want verified claims. You can't assume the doctor is allowing sick people to stay at work since you have no evidence he's actually doing that. Otherwise he's essentially just extending the clinics services for free as a favor to employees, which is legal, but it's up to you if you want to accept that or not. I wouldn't accept a "physical exam" from my boss, but in reality it's probably more of just a casual take your vitals and write a prescription type of exam, which if you think about it isn't that big of a deal. Regardless perhaps you just take this job for a short period until you can find something better. Otherwise I don't know what your resume looks like so it's hard to say if you could find something better without more work experience. If you need medical insurance at some point you can just get it through the ACA, which is expensive, but it's a temporary solution.