The short answer is yes, the HOA has a duty to treat all of its homeowners equally and to enforce its protective covenants equally and fairly. Sometimes that is simply not the case though. It would be interesting and important to find out why the HOA made an exception for this particular homeowner and whether they went through their proper procedures (including board approval) in granting a variance. I would consult with an attorney next week. Best wishes
The information provided in this answer does not create an attorney-client relationship. If you are interested in his legal services, feel free to call Chris at (303) 409-7635 at his law office in the Denver Tech Center. All initial consultations are free of charge.
The HOA would need to formally address the issue at a meeting and agree to amend certain HOA documents in order to give this homeowner the setback asked for if it is at odds with the existing regulations. A local lawyer can help you review the HOA governance documents and minutes of the HOA meetings to make sure that everything has been done accurately.