Should I feel bad about I've done?

I work closely with a coworker and I know she is a good person, she doesn’t work very efficiently, though. She often complains that she has too much to do. Myself, however, somehow don’t get enough workload. I help her with some of her work meanwhile learn from her because I am new and nobody trains me. She will be gone for the next two weeks and she wants me to fill her in while she is away. So she started to send people emails asking them to contact me about one job she does. Before this and after I learned that she will be on vacation, I had asked the assistant controller if he wants me to do that particular job, but he didn’t say anything. I don’t mind help her out. However, I resent the fact that I was not instructed by the management, but her, to do her job while she is gone (she holds a lower position than I do, but she asked me to do work including some data entry work for her, which makes me feel that I work for her). Besides, I feel it is the responsibility of the management, not either my coworker or myself, to make certain that the department’s operation not be disruptive while somebody is absent. So I brought up the topic to the assistant controller, for one thing, to remind that they should have a plan about who should do my coworker’s job, for another, to confirm that he does want me to fill her in. To our surprise, the assistant controller doesn’t want me to do my coworker’s job while she is gone. He said the job can be waited till she comes back.

My coworker was quite upset. She probably feels that I betrayed her, because she often mentioned that how much she enjoyed working with someone in a team and helping each other, and I told her I feel the same(which is the truth). She thinks that I don’t want to help her. I thought what I did is help her out too, because she often complains she is doing too much but not appreciated and she needs help. By bringing this to the attention of the assistant controller, making them aware that she was assigned an unreasonable workload may get her the help she needs. I tried to explain but I know she was not convinced. Now I feel pretty bad. Is what I did is inappropriate? What should I have done?