Does an HOA have any legal rights?

Yes, they can take you to court, and in most states they have a pretty clear path to do it. When you bought your home in an HOA community, you signed the CC&Rs, which is a binding legal contract. Structural additions like a larger deck almost always require HOA approval, and building one without it gives them grounds to pursue fines, force you to tear it down at your expense, or sue you for non-compliance. Your neighbor not getting pushed on the mildew notice is not a reliable indicator of how your situation will play out. HOAs tend to be a lot more aggressive about unapproved structural changes than they are about maintenance notices. A bigger deck is visible, permanent, and requires permits. That is a very different situation than a mildew warning that got ignored. There is also a practical issue down the road. When you go to sell, a title search will surface any HOA violations and unapproved structures. Buyers, their agents, and their lenders will flag it, and you could be forced to remove the deck or resolve the violation before closing anyway. The better move is to appeal the decision. Request the specific language in the CC&Rs they are citing, find out if there is a variance or appeal process, and consider presenting revised plans that address their concerns. Many HOA rejections on first submission are not final. Push back through the proper channel before you pick up a hammer.