For most government related purposes (SSI, SSD, Medicaid, etc.) it is not considered a disabililty in the U.S. It is considered a disability in all U.S. educational institutions - you can request services or accommodations. It is also considered a disability under the ADA - if you tell your employer you have it, you can request "reasonable accommodations" and are protected from discrimination in theory (but rarely in practice).
Yes, medical records are private. However, there are many ways in which this privacy can be reduced. Often, doctors require new patients to provide their records from past doctors. Or they "strongly encourage" it by requiring lots of expensive tests if you don't share your records with them.
It's similar with insurance companies. Some require you to submit your records as part of the application and then decide what to charge you based on this, or turn you away if you're too costly.
Others only see what the doctors bill them for while you are covered. They could find out you have AS if they get billed for an AS-related doctor's visit and the doctor writes that AS was the reason for the visit. This could affect what the insurance company charges you in the future.