Without commenting on whether any particular party was correct in their clinical assessment:
About once a month, the Diving & Medicine section of ScubaBoard erupts with someone asking about a question re the risks of diving with a particular disease or disabling condition. People opine without specific information about the individual's symptoms, etiology, or degree/areas of impairment and make broad-brush proclamations re who should or should not dive. This leads thread participants to assume extreme positions that are invariably inappropriate over-generalizations, which in turn leads some folks to decide to hide or ignore key medical considerations, and others to then offer extreme misinterpretations of the Americans with Disabilities Act.
Although the sequence of events may well have included other components which, in the interest of brevity, Drew may have omitted, please consider the following probable flow of events:
- Student presents with bona fide medical clearance (whether the oncologist is correct or not is not the issue: the oncologist made an expert clinical determination);
- A well-intentioned individual who is not a physician second guesses the individual who is a physician;
- The well-intentioned instructor gets another physician to opine based on little more than a diagnosis and not based on a clinical assessment of the patient him/herself and a comprehensive review of the patient's medical record.
- The well-intentioned instructor shuts down the discussion by refusing to provide a service.
Rather than encouraging the individual to sit down with the dive doctor and his oncologist to develop an informed assessment (as JBD has wisely suggested), this approach only encourages the person to "shop around" for another instructor who may be (1) more open-minded, (2) less concerned about student safety, or (3) less informed re medical aspects of diving. It may encourage the student to hide the details of his medical condition and perhaps make an uninformed and potentially risky decision. And if, as the diving doctor has opined, lung cancer (treated or in remission, we don't necessarily know which) is an absolute contraindication for diving, the oncologist will never learn that and may blissfully continue to clear others. It just seems to be a formula for resentment and disaster.
I think JBD laid out a much more appropriate and responsible approach, since in the final analysis, it should be an informed individual that makes the decisions re diving, NOT A WELL-INTENIONED INSTRUCTOR OR A LDS OWNER OR A PHYSICIAN THAT HASN'T PERSONALLY EVALUATED THE PATIENT OR EVEN THE ONCOLOGIST!
One other consideration which, while it may not apply to Drew's situation since he is working in the Cayman Islands (everybody let out that sigh of envy!), is relevant here in the states. If, as I might guess, the potential student's oncologist wrote certain medical information on the clearance/approval sheet, it must be regarded as a medical record which cannot be released to a third party without the express written permission of the patient. You may say that the student gave it to the instructor, so the instructor has the right to do whatever he wants with it. This is simply not the case. I am not a lawyer (and I don't play one on TV), but I might wonder if this information and document is subject to the HIPAA regulations, which for the first time sets specific federal penalties if a patient's right to privacy is violated (fines up to $250K and/or imprisonment up to 10 years for knowing unauthorized disclosure/unintended use of individually identifiable health information).
Drew, I don't for a minute doubt that you had the best intentions in securing the second opinion and it may indeed be that lung cancer (treated or in remission) is an absolute contraindication (perhaps some of ScubaBoard's venerable physicians can provide us with some additional information!), but please recognize that you are participating in a "medical transaction" in which all parties have certain rights and responsibilities. You may say, "but what about my rights as an instructor or a LDS operator?" While I can't speak to the laws of the Cayman Islands, here in the states, Title III of the ADA sets the rights of the person with a disability and those of the "public accomodation" (which in the Act is legal-speak for a public business):
36.202 Activities.
(a) Denial of participation. A public accommodation shall not subject an individual or class of individuals on the basis of a disability or disabilities of such individual or class, directly, or through contractual, licensing, or other arrangements, to a denial of the opportunity of the individual or class to participate in or benefit from the goods, services, facilities, privileges, advantages, or accommodations of a place of public accommodation.
One may ask if there are exceptions established in the law. Yes, but "instructor wanted to protect the person from potential risk" isn't necessarily one of those exceptions. Re that risk, right now all we know is that the two physicians have disagreed on the magnitude of risk. For a LDS owner to accept the physician's opinion that he/she finds more compelling still has the net effect of violating this "right to participate" provision of the Act.
I certainly don't wish to leave the impression that I would condone diving for someone whose disabling condition created an unreasonable risk of harm to self or others. But the practice of medicine and the laws of this country do not make this situation as clear cut as some might want to think.
I definately would take the advice of a dive physician over just a regular physician any day of the week. However the reality is even if you had let the student dive, if something had happened the oncologist would of been held liable as he signed him off. 
