That drives me bonkers! I'll get calls from other departments trying to transfer someone to me and they are supposed to explain the problem before they send the call. A lot just send it over without any introduction of heads up which makes us look bad when I discover that the issue is solely the province of the other department and have to send it right back. I figure those people just want to get rid of the call. Then there are the incompetent people who do take the time to thoroughly explain what they need me to do. Only what they want me to do is completely and entirely their job. I don't have access to that information, I have no way to answer the question or do those actions for anyone. It's not even nuanced - I handle content and substantive work for the clients we already have. They handle getting more clients and the money. And yet they sound shocked that the client was in fact already in the right place.
I had a situation come up when I worked in a military hospital where someone was transferred to my number by accident (or maybe whoever transferred them just wanted to get rid of them. I don't know.) It was an ambulance driver who was there to pick up a patient, and he didn't know where in the hospital the patient was. Unfortunately, it was at 7:30 in the morning, during most shift changes. I tried to transfer his call to the places where he should have been transferred, e.g. the transportation people, or, failing that, the charge nurse. No one was answering the phones. The driver had always been polite and had thanked me for my help; finally, he called me back and said, "I hate to keep calling you, since I know you don't have anything to do with this, but no one else is answering their phone." That time, between the two of us, we were able to figure out what floor the patient was on, and I was able to send him to the floor's nursing station. I never heard from him again, so that must have worked.
Because of where my department name was located on the "list of department phone numbers" the information desks had, I would often get calls for the transportation people (I was transcription.) Some, like the ambulance driver, were polite. Others were downright rude; one rude person asked me why I had answered the phone since I wasn't the department they needed. Or something like that. Like my phone only rang when it was for me. Sheesh.