Who is ultimately in charge and calls the shots? The paramedic, or a chief officer on strictly a medical call?
The answer is, of course, it depends. State laws, agency policies, local medical direction can all influence stuff.
As a general rule, there are two ways to be "in charge," operationally, and clinically. Clinically, it is usually the provider with the highest level of medical training (medical director, paramedic, RN, etc). Operational, it is the provider with the highest rank (chief, captain, supervisor, etc). So the question of "who is in charge" doesn't have a clear cut answer.
Many years ago, I was on a fire department, that provided ALS first response. the Captain on the shift was an AEMT, and his driver and firefighter were both paramedics. who was in charge? Well, the captain wrote the paperwork, and the FFs did the patient care. you can argue that one as to who was in charge of the situation.
Also keep in mind, if the chief in question says "you will assess this patient, and run a 12 lead," that's a fair directive to give you, and TBH, it's probably easier to follow his orders instead of butting heads. Now if he says :"you will give the patient medication x, y and z" and you don't think they are indicated, then say (respectfully!!!!) that you don't think it's necessary, and file a clinical complaint with the appropriate person at your department. And if he pushes you to, then give him all the equipment and let him do it, and follow up with the appropriate person afterwards.
The real question is why are you butting heads with a chief? especially on a scene? if you have an issue, it should be brought up through the chain of command, during a prescheduled meeting, with the Chief of the department if needed. If he tells you the ranking operations office is in charge, then have him show you the SOP (ie, put it in writing), and that's that. if he says the highest medically trained person is, well, that's what, have him show you the SOP.
Asking random people on the web might get you the answer you want to hear, but if that's not how it works at your department, than it's irrelevant to the situation.