Legal Question in Real Estate Law in Georgia

You are correct. The HOA cannot enforce that rule.

The FCC's "OTARD" (over the air reception devices) rule allows for HOAs to draw some reasonable limits on the location of satellite dish antennas. The association can enforce the restriction if it complies with the rule. There's a FAQ on the FCC's website that gives a good deal more information. The actual wording of the restriction the HOA seeks to enforce as well as how they apply it matter. If you are in a condominium, there's even more to the analysis and the association likely has even more ability to control your ability to install a dish.

If the FCC's FAQ is not helpful, and you can't get past the association's refusal to let you install a dish, I'd suggest contacting an attorney with experience in this area. They can help you (and, hopefully, the association) get the situation worked out.