First, I would find out what is the something of "concern" that they are referring to and then check to see if they can legally deny you based on their "concern". They have abide by the rules of Fair Housing and other state laws. If you have something in your credit history they can deny you because the association might be worried about you not paying your HOA fees. Find out what their concern is and speak to them about it. Good Luck.
No really they have the power to accept or to decline your application the only thing need to check if you maybe can ask them for your credit report and background check they did for you and check what is that showing