Simple answer really. You have to undertake an annual dive medical. No in date medical card, no dive.
A medical testing...what, exactly? The concept of an annual physical exam for general practice is a pretty uniquely American institution, far as I can tell (it has no strict place in how I practice medicine in The Netherlands). Specific screening for treatable risk factors, sure - i.e. weight (which you can do yourself), blood pressure (GP, or buy a meter), cholesterol every once in a while, and evidence-based screening programmes for various forms of cancer (i.e. PAP smears and breast exams for women, and there are pilots here for colon cancer) which are organised on a national level. A cursory search of the evidence indicates that there's really no good evidence base for most of the rest of a physical, let alone a good evidence base for a 'dive physical' in the absence of manifest symptoms or disease.
Adding to what my colleague mentioned about the Bruce treadmill test - when used for determining coronary disease at least - it is a notoriously poor test in terms of reliability in a broad range of subjects, and should really only be used in patients with an intermediate pre-test likelihood of having occlusive coronary artery disease and a normal baseline ECG, where it has reasonably good specificity and sensitivity. Current European and ACA/AHA guidelines are not all that hot on exercise testing in low-risk patients, and pretty much all of the evidence has been collected in people who are at least suspected of having angina pectoris.
Don't get me wrong, preventive medicine is extremely important, and should be guided by evidence; raising awareness and increasing self-management are essential, along with controlling other modifiable risk factors with medication, where appropriate. However, getting a 'full physical' may provide a sense of security to people without specific symptoms. When undertaking something like Scuba, understand the risks involved, be in as good shape as you can, dive within your limits, but understand not all accidents are preventable.
Any mandatory physical for something that mostly entails personal risk (i.e. scuba, rather than piloting a plane) should, IMO, have proven benefit it terms of preventing serious incidents or mortality. Otherwise it's just another useless exercise in unnecessary diagnostics and examination.