Before divers start their work underwater, the Association of Diving Contractors International recommends a preemptive medical exam. The exams don't stop there, though: the association also requires divers to undergo regular exams throughout their careers. This is especially important when commercial divers returns to work after a serious illness has kept them out of commission.
ADCI Guidelines state that, unless there's a law saying otherwise, divers need to be re-examined if they've been hospitalized for at least 72 hours for a "diving-related injury or illness." The type of examination can vary depending on the diver's physical condition, but most cases, the word of a physician is necessary before the diver goes back to work underwater.
Some of the medical exams test specific qualities, such as visual perception, or illnesses like sickle cell. The National University Polytechnic Institute lists some of the benchmarks for each of the individual tests. In some cases, a condition can only be debilitating if it passes a certain benchmark. For example, the source says that a 35 dB or higher hearing loss is possible cause for outside opinion, but not necessarily for disqualification.
In an article for Underwater Magazine, Dr. Brian Bourgeois described the layout of the form for conducting diving physicals. He said that it involves both a very detailed medical history and a series of things that would "complicate a diver or exposure to hyperbaric conditions." Some of the disqualifying conditions the ADCI lists include seizure disorders, "significant" nerve damage and any ailment that requires continuous medication.
Commercial diving contractors could prefer insurance from a source that understands the industry, unlike many other general providers. This may include the many health hazards that divers find themselves exposed to.