Something of this nature happened to me as well, and I did a combination of the things mentioned. I am not a driver nor a crew chief, so my entire life is spent in the back of the rig. However, I was working with another Basic (newly certified) who was also in the back with me, and she felt the need to inform me that I was going to be the "vitals taker" all night, and she would handle the rest. When our first call came around, she was struggling with connecting leads and basic things like that. I offered to help and she told me to "stay in my chair and do what I was told." Basically I let her struggle through that call. When we got back to the squad room, I calmly told her that she can't order me around like that, especially after such a poor performance on that call. She glared at me and left me alone for the rest of the night.
The next day I reported the incident to management and found out that she had done it to people even when she was not an EMT and doing her clinicals.They got her off that shift immediately and she was reprimanded.
Sometimes if the person is not willing to make a comprimise, going to management is a good move, but in my opinion it's also ok to remind that person that you are not to be pushed around.