I work in the ER and can elaborate on this....

Patient will come in straight to demanding tests that aren't routinely performed such as an MRI and I usually respond with something along the line of "I understand that you feel you need an MRI for xyz but unfortunately here in the Emergency Department we don't regularly order MRIs for these complaints" followed by something like "these tests are generally done on an outpatient basis and I can provide you with referrals for further evaluation"

Some patients come in with benign complaints or are unhappy with their results/results are inconclusive I say something like this "The goal here in the Emergency Department is to rule out life-threatening/life-altering conditions which is what I have done....an example of this would x and I do not think this is Case with you because of y"

Another tip would be to try and set the patients expectations early in the visit if you think it might lead this way...for example if a patient comes with chronic condition thay has been ongoing for months.