If they do, in many of those countries you will likely become a very rich man. So long as you did your part by answering the questions on the relevant medical honestly.
You are required to answer questions honestly and submit to a medical examination. So I am assuming this scenario would apply to a condition which might decertify you under CAD rules yet permit certification in the other country.
Most real nations have fairly strong health privacy laws. Breach of these is always a civil and sometimes a criminal offense. There might be some limited cross flow allowed when it can be demonstrated there is a bona-fide and imminent threat to the safety of self or others. But disclosure of protected information is an absolute minefield for a company in some developed nations.