My aunt had a condition that causes fluid build up in her brain. She has a slightly unusual shunt arrangement, and over Christmas (we now know) it got blocked up. She started developing neurological symptoms, and the only person who knew enough about her treatment to be able to sort it out was her doctor.
The actually had his home landline number, but he was away, and it was only due to luck of a call coinciding with the neighbour feeding the cat that they were able to get the number of where he was for Christmas. By that point, my aunt with unconscious in hospital, and might well have died if treatment had been delayed any more.
It's scary that sheer happenstance saved your aunt's life. I wonder how medical record keeping could be improved to help with that scenario.
In this case I think it was less knowledge of the particular case, and more the expertise in that specialised situation. Skillset rather than records.
There are a few special patients he'll give his cell number to. Pregnant moms especially I think. He's a country doc and the only good baby doctor within a hundred miles, so if there's an OB patient who he thinks is higher risk, and who he knows won't abuse his cell number, he'll give it to them no problem.
There's no medical reason for a doctor to be on-call 24/7/365, and it's stupid to expect them to. If an urgent medical issue comes up at 2 AM, the patient can go to the ER, which is what the doctor would tell them to do anyway.