If they’re willing, or compelled by necessity, to dial numbers by hand, they can and do call cell numbers.
You can register both landline and cell numbers on the Do Not Call list, but that won’t block some categories of calls.
Aside from all that, you can always investigate a mystery number without calling it back. If it is an autodialing telemarketer, it’s almost certain you can identify them without dialing or answering it.
I never call back a single unrecognized number. However, I will occasionally get repeated calls from the same number. One time I got six calls from the same number in two hours. I called them back, informed them that they had the wrong number, and asked them to stop calling me.
If it shows up a few times, I might, but usually not. I sometimes call numbers with a local area code, because my cellphone’s number is still from up north, so I know it’s probably not a wrong number. But mostly, no message=no callback.
If we call the number is blocked, and any messages left have to be very generic “Hi this is Dr irishgirl, please call me back as soon as you get this”, so that if challenged by a third party the patient can say that we called the wrong phone and they certainly never went to see the doctor or if I really did call the wrong number that nothing confidential is said.
An unrecognised or blocked caller ID and a confusing or absent message might be your doctor trying to protect your confidentiality.
I had a call a few years ago from a someone I needed to chat with, and his message was garbled, so I called the wrong number when I called him back. (He said he was leaving the office and I should call his cell, then the message was hard to hear.)
When I realized that I had dialed a wrong number, I said: I’m sorry, I have the wrong number. Then I hung up.
The man called me back daily for over a week demanding to know who I was and how I got his number. He left threats to call the police, left threats to come and “get me” and was just an all-around ass.