Your brand is your reputation. Gatorade is performance. Sony is style. When your customer service is lacking, your reputation/brand will take a hit. When you improve your customer service, your brand/reputation will see a lift. AT&T is now offering excellent customer support on Twitter and naturally they are seeing a brand lift. I'm sure their increasingly capable customer support via traditional channels will continue to improve their reputation as well, but the highly visible nature of social really gives this lift a boost.
I have been an AT&T wireless customer for nearly four years. I switched over after a poor customer service experience with Verizon. I haven't had the smoothest ride with AT&T but have stuck with them through it all. Their customer service used to be horrible. I dreaded having to use their customer service. More recently however, their customer service has been stellar. This isn't just about Twitter, it's about a meaningful conversation.
Should AT&T be offering customer service on their Facebook Wall? Probably not. This is their most visible real estate and probably not the best area for inviting complaints. Is it great for both AT&T and their customers that they are offering strong customer service online? Absolutely!
Are AT&T's brand issues resolved? Nope. No matter how much AT&T invests in customer service, it will not resolve people's frustrations with their network or with troubling policies.
Is AT&T's customer service offsetting their network flaws? I'm not sure, what do you think?