In America at least - if an op were to deny services to an elderly customer, regardless of any "we reserve the right to refuse service to anyone" signs or policies, they run a serious risk of an age discrimination lawsuit. Merit or not, reasonable or not, it's a goodly risk to consider. Many times, an op might provide services against its better judgment, and simply hope nothing happens.
That is not true. In the USA, any dive op has the final say in determining who can and who cannot dive on their boats. They are the sole arbiters. Provided that their determination is not based on anything other than ability to safely participate, they are well in their rights to refuse service to whomever they please. This applies to overweight, elderly, infirm or unruly customers. This has been demonstrated repeatedly in law at amusement parks and other forms of recreational activities.
Any operator may turn down a customer for safety reasons. Following your logic, an insurance company would have a fabulous time denying coverage.