One, in some of the countries I know (with universal healthcare and no centralised records) you don't go to a random doctor. You have a declared family doctor and you have to go to them unless they are unavailable, in which case the other doctor you go to has to declare that you couldn't go to your doctor. It's a small hurdle to prevent doctor shopping, but it means people are more likely to always see the same doctor. Specialists are given the relevant information by the family doctor when referring a patient to a specialist, and in most other cases records are not really needed, or the ER will contact whoever to get the information they think they need. It might sound hazardous but in practice it works fine.
Second, some places have centrally-stored records but the access is controlled by the patient. Every access to the record is disclosed to the patient and he has the possibility to revoke access to anyone at any time. That generally goes together with laws that fundamentally oppose any automated access or sharing of these records to third parties.
And third, I don't understand what any of this has to do with who whether healthcare access is universal or not? Universal healthcare without centralised records exists (in France, unless it has changed in recent years, but it at least existed for 60 years or so) and centralised records without universal healthcare could exist (maybe privately managed by insurance companies, since the absence of universal healthcare would indicate a pretty disengaged state).
One, in some of the countries I know (with universal healthcare and no centralised records) you don't go to a random doctor. You have a declared family doctor and you have to go to them unless they are unavailable, in which case the other doctor you go to has to declare that you couldn't go to your doctor. It's a small hurdle to prevent doctor shopping, but it means people are more likely to always see the same doctor. Specialists are given the relevant information by the family doctor when referring a patient to a specialist, and in most other cases records are not really needed, or the ER will contact whoever to get the information they think they need. It might sound hazardous but in practice it works fine.
Second, some places have centrally-stored records but the access is controlled by the patient. Every access to the record is disclosed to the patient and he has the possibility to revoke access to anyone at any time. That generally goes together with laws that fundamentally oppose any automated access or sharing of these records to third parties.
And third, I don't understand what any of this has to do with who whether healthcare access is universal or not? Universal healthcare without centralised records exists (in France, unless it has changed in recent years, but it at least existed for 60 years or so) and centralised records without universal healthcare could exist (maybe privately managed by insurance companies, since the absence of universal healthcare would indicate a pretty disengaged state).