Group fairness and privacy are fundamental aspects in designing trustworthy machine learning models. Previous research has highlighted conflicts between group fairness and different privacy notions. We are the first to demonstrate the alignment of group fairness with the specific privacy notion of attribute privacy in a blackbox setting. Attribute privacy, quantified by the resistance to attribute inference attacks (AIAs), requires indistinguishability in the target model's output predictions. Group fairness guarantees this thereby mitigating AIAs and achieving attribute privacy. To demonstrate this, we first introduce AdaptAIA, an enhancement of existing AIAs, tailored for real-world datasets with class imbalances in sensitive attributes. Through theoretical and extensive empirical analyses, we demonstrate the efficacy of two standard group fairness algorithms (i.e., adversarial debiasing and exponentiated gradient descent) against AdaptAIA. Additionally, since using group fairness results in attribute privacy, it acts as a defense against AIAs, which is currently lacking. Overall, we show that group fairness aligns with attribute privacy at no additional cost other than the already existing trade-off with model utility.