I know a few people who have had experience with both. I personally have dealt with HLLE from high nitrates in a tank (high in tap). It is nearly impossible to provide "definitive proof" on basically anything....But I can show experiences that show what I said. You can't say "oh, well that doesn't count" when I link an article....that's asinine....
Nigel is right. You can't just say oscars don't get HITH either really. As Nigel stated its all over the place with HITH and HITH related articles.
What I do know is that HITH is most commonly known also as hexamita which is indeed a parasitic infestation as you pointed out however, this manifests itself in many a species intestinal tract including cold and saltwater fish but for freshwater it seems to be cited as predominantly found in cichlids.
I just experienced hexamita in my tank or an illness which almost certainly fitted the bill for hex, emaciation, white discharge, loss of appetite but most notably the first signs of manifestation began with the pits that look very much like the ones in the posters photograph.
I believe HLLE is a variation on the same pitted head symptoms where the parasite is not present and is caused by poor water quality. Hex on the other hand although most certainly will not be helped by poor water quality may not necessarily be indicative of poor water quality and also requires in serious cases where the fishes immune system cannot contain the parasite, medical intervention. Internal and external administration of metrodanazole would be a good start if hex symptoms are observed.
I'm cleared now. I must note also that feeding a food with vitamin C seemed to have accelerated the recovery although your mind can easily be tricked in this hobby, the recovery could have been down to the meds alone.
The hex parasite came with a fish I added it was already looking 'different' but I figured that a couple of weeks in clean water would see it recover. Instead it transferred itself on to 2 other fish that had to be euthanised before I could get it under control. I believe it is passed in the feces and/or white discharge. The feces will be white also.
The external med will destroy the free swimming parasite and the internal med will take care of the parasite in the tract. Water changes will help remove free swimming parasites further.
If it is just HLLE (sometimes seen together with HITH, which may be where the confusion arises?) with no hex symptoms, extra water changes and a high vitamin and veg diet may be all that is necessary.
Hex is nasty and needs to be dealt with immediately. Fish that no longer eat need to be euthanised IMO.
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