I have never been asked for full records - either by AME or CAA.
Your AME(and the CAA) has the right to ask for more information on any subject that they may have a concern about - treatment history etc.
Many people don't have a full medical history either because they've never had or needed medical care or because they have moved around a lot and it is fragmented. They can't have what you don't possess.
If you go to a new AME having filled in the questionnaire (in UK anyway), you don't list any significant medical history and you appear to be generally fit and healthy then the AME will probably take it at face value as long as he or she feels you are being honest with them.
On the other hand if you walk in with bloodshot eyes, wheezing and try and pass off the large scar on your chest as a birth mark and then are cagey about your medical history then expect some questions to be asked.