Hi, I am not familiar with the term Graphite disease. I do know fin rot is common. Fin rot can be caused by anything from Mycobacterium, colomnaris, to just flat out poor tank conditions. There are so many diseases caused by fungal, bacterial, and parasites, and the like. I was just told the other day that a lot of fish coming into the U.S. carry the parasite Hexamita. This is a slow killer, as it gets in the gut and robs them of the nutrients from their food. Their fins will thin out and could 'rot' from this as well. Sometimes a fish has a particular pathogen, and the outward signs are a secondary bacterial infection. I think the biggest problem is everyone assumes the fish is healthy because it looks good. Another problem is many people have more than one betta, and they cross contaminate from one tank to the other as I mentioned. No one just treats them when they come in, like we do goldfish or catfish for example. Just because a fish looks good on the outside, don't always assume it is healthy on the inside. Parasites lie dormant and wait for that right moment. It might be someone misses a water change or two. Gets a little spike of ammonia or nitrates go up. This weakens the fish's immune system and boom...sick fish...
Oh, Hex and I are very familiar foes, lol! I had two guys who came down with HITH, and in the process of reading up about the treatment the Hex information came up (on a cichlid forum actually, apparently this is common in that type of fish). Basically, what was detailed was that HITH is not actually a disease, it's a side effect of the parasitic nutrient robbing you mentioned that causes actual wearing of the structures in the head that causes the holes. Fortunately, my guys were able to get better through a course of praziquantel, removal of *all* carbon from the filters (because the carbon was absorbing even MORE of the nutrients, so even less available to the fish), and massive doses of vitamin c. It was a fight, but one that I seem to have won...at least for now. :) Geoffrey is going on 3 years now, and it's been a year since his Hex. His tank mate, Chaucer, made it to two and a half or so before his death of presumably old age (he had no disease signs, he just sort of faded away), but he was a petstore rescue cup purchase who had such high ammonia his scales were sloughing off when he came home...so I figure having made it to two was a pretty good run for the little guy.
The "graphite disease" is something that pops up every now and again on here in the disease section, and I believe the term is colloquial to this forum. It's a weird sort of horrible fin rot that strikes very, very quickly, and kills almost 100% of the time, even with some hefty treatments. For whatever reason, it hits blue bettas, and they're fine one day, then the next they're showing this weird silvery gray in a section of fins. Within a few days, from what I've seen on here, even with a variety of treatments, the fish is dead, the rot having spread mercilessly quickly up the fins and presumably into the body.
There are debates on here that it's some sort of myco derivative, or some sort of really nasty fin-rot, almost like necrotizing fasciitis in people. To my mind the fasciitis makes more sense...but, again, that's just an opinion/gut feeling. The strange part is that it even hits people who are known for keeping *pristine* tanks...and fish who have lived in those tanks for months, even a year or more. There doesn't seem to be any correlation between keeping a beautifully clean and well-cared for tank and being spared from the disease. I'm sure a dirty or uncycled tank would definitely contribute to the likelihood of disease (this or any other), but it doesn't seem to be the cause the way normal fin-rot seems to be tied to dirty tanks.
I've got a large sorority, and I can also attest to the changes in water condition bringing down a presumably healthy fish very, very quickly. The stress of living in the group combined with, as you mentioned, any sort of water quality blip...and someone is starting to clamp or hide until the issue is corrected. On one hand it's rough, because you're always just waiting for something to hit...but on the other side of the coin, it's immediately obvious that there's something not right even without seriously frequent water testing. They're good little barometers of water quality. I know what you're saying though about cross-contamination. Since all my guys come from petstores...I just always assume they're carrying just about everything under the sun and wash/QT accordingly.
Oh, and this is completely random, but I love the goldfish in your avatar! ;) I love goldies...one of these days I'm going to get around to setting up a 100+g goldie tank (I figure if you're going to go big, go on ahead and go really big so that you can have room for a few, lol!)...but I haven't quite made it that far yet. :)