Hello Joe,
Yeah, the reason the leaves were dieing so fast, is because the plant was responding to the infection. There are a number of issues at work here. First, the disease got started by poor conditions. Most of the time a plant with a functioning immune system can control the disease until the conditions improve to the point they no longer support the pathogen. This is what most people are reporting here, but they aren't aware their plants were being attacked in the first place and just associated the systoms with poor conditions, not a pathogen. Your plant was weakened in some other way which allowed the pathogen (most probably a fungus) to spread too quickly and it started to overwhelm the entire plant. I have seen this happen to lowlanders that were kept too cool and wet. One thing a plant does to control pests and disease is to prematurally kill the affected areas, limiting the pest's or pathogen's ability to abtain food and in turn reproduce. This is why the leaves were dieing so fast and why the color of the leaves was changing to yellow and then black. The normal death of the older was replaced with an emergency response by the plant, if allowed to continue without treament, it probably would have led to too much of the foliage die off, weakening the plant further and then general rot could set into the stem, killing the entire plant, or forcing it to grow back from the root stock--if it still had some strength left in it.