Im not only a EMT (soon to be Paramedic) but also in the Sheriffs SAR here. I tend to respond to any emergency I see regardless of on duty or not, no matter what. However, in my vehicle (or any Im riding in at the time) I always have at the least my ball cap (Sheriffs Department Search and Resuce Medic) and if possible my uniform shirt (Sheriffs Dept. patches, same basic uniform, just organge instead of black), trauma bag with a star of life and "Sheriff Search and Rescue" on it, my Sheriffs ID card, orange vest saying Sheriff Medic and sometimes my badge. I typically always wear boots and bdu's if not my complete uniform. I do off-duty patrols during peak times to alleviate the needs of the department.
The point is I have a buddy who wanted to be a cop, firefighter etc. all his life but never did it. When Im doing off-duty patrols, he comes along and helps out. He tries to claim he is with me, giving off the appearance of being in the Sheriffs, a medic or whatever. I always call him on it but it causes problems for me, someone who is legitimate and trying to help. Thats why I always try and be ready because around here, a big metro area, people, especially PD, SD and FD, are weary of others. My friend doesnt help that.
The moral of this is always carry around your uniform or at least ID. I never accept the help of someone unless I know they are legit. To much a liability. My buddy usually just does crowd control or gets me supplies. I never let him do anything medical (except help in CPR which he is certified).