Everyone seems to be forgetting that Annie has always been like this. She was originally sent to spy on Aria, but Aria won her over by appealing to her shallow ambitions. She gave her a few dresses and let her sit at the table to eat snacks, and that small taste of nobility was all it took to flip her. Annie's always been mildly shallow and greedy, even if it's not malicious, it's just how things are when you grow up with nothing and spend every day surrounded by luxury that isn't yours. It was so surface level that it was easy to get her to accept it.
While there is some truth to what Aria's spittin', it's not a truth that would work on everyone. For instance, consider her teacher, the hot needleworking pure-hearted oneechan who is marrying upwards. She's gaining social status from her marriage, but I bet this same argument would be rejected by her because her ideals and sense of self are so different from Annie's.