If you are going to the chiropractor 26-52 times a year, there must be some sort of issue? Most people don't go to a chiro once a week for fun. I would be surprised if your chiro would write a letter saying there was nothing wrong if you are getting treatment that often, but I'm not a doctor...
Should you care? Well, that depends if you care about the disability insurance, which is usually something people care about as it's one of the most important types of insurance you can have....will it effect your insurability in the future for other types of insurance? Probably not as you can always explain why you were declined. It's not like if you apply for other underwritten insurance based on health that they won't write to your doctor anyway.
Usually the disability insurance you can get through a group isn't very comprehensive and has more coverage holes than swiss cheese, and just because you were declined by one company doesn't mean they would all decline you. Would be helpful to know what your chiropractor has to say about the diagnosis though...
Disclaimer - I am an independent insurance agent. If the above message contains insurance-related content, it is NOT intended as advice, and may not be accurate, applicable or sufficient depending on specific circumstances. Don't rely on it for any purpose. I do encourage you to consult an independent agent for insurance-related advice if you have a question that is specific in nature.