We have never seen on the threads anyone with "normal" diabetes or hypertension (without complications or flare-ups requiring extra intervention) - that is, someone whose condition has been diagnosed some time before and whose regular treatment is controlling it so they live a normal life - being refused entry.
If a Medical is referred, the MA's responsibility is to look over it and understand the applicant's condition as far as possible. The history given MAY be enough, or they have the power to require a report from the person's own doctor or a specialist, or more tests if appropriate, so that they reach a satisfactory understanding and can make an educated guess about the person's future health (and therefore, costs). For the conditions you are asking about, widespread and commonly treated with known medication, usually the most that is required is that their regular doctor says they are doing well on their current regime.