Do you stop CPR to assess for a pulse yourself when your partner tells you there isn’t one?
I think this is probably the most basic example of this. Patient condition: cardiac arrest. do you trust your EMT partner or (gasp!!!) a firefighter to be unable to find a pulse? This is, of course assuming there aren't any other signs (patient is breathing, patient is saying "stop that hurts", etc) that would give you a hint that what you were told and what was actually happened were not the same (successfully intubated patient with a ETco 2 with no waveform).
As a general rule, when I was on the ambulance, unless I knew a firefighter had previously worked on an ambulance, there is a high probability that I am going to ignore almost everything they say, even if they are EMTs. Let me copy the demographics from you, and stick around if I need help carrying. They often mean well, but many of the firefighters I have met are horrible EMS providers.
Now that I'm down south, and the FDs go on more EMS calls, and actually fall under the county medical director, I have a little more faith in their abilities.... but unless they work or have worked on an ambulance, I am going to thank them for their assistance and do my own assessment. Been turned too many times in the past. And now that I'm no longer on the ambulance, when EMS arrives, I am totally ok with stepping back, letting them to do their thing, even if it means redoing everything I just did.
but if you can't trust your partner's abilities, than either you have trust issues, control issues, or the agency has training issues if they can't do their job properly. and a good partner does know when to have someone else confirm their findings, especially when they seem off (against, assuming you are the same training level; if it's a B/P crew, than the P is overall responsible and more educated, so I can see why they wouldn't trust an EMTs interpretation of an ALS skill).
If I was the medic, about to perform a highly invasive treatment, I'd probably want to verify for myself before I did something. cardiovert, needle decompression, various medications that are high risk / low frequency (but still appropriate when the patient's condition warrants it) such as amiodorone, sure, but if my partner says "hey, i think it's a stemi, or a stroke, or a trauma alert, or a 'hey, i think i see the head'," then no, I am going to trust their assessment and make the appropriate notifications and transport decisions.