A Question about Tense Agreement

In school we learn about tense agreement, but I am often confused as to whether or not we must use tense agreement in some sentences. While reading an entry a short while ago, I came across the following sentence: "She told me that she had been having a mental disorder since last November." According to the author, she hasn't recovered from the illness.  I suppose the author may have used tense agreement, but doesn't it sound like she has already recovered from the illness?  Two native English speakers corrected the entry, but neither of them corrected the sentence, so I might be wrong. I'm just curious.