You're right - I'm looking at it from a particular perspective which *may* be wrong. But then, all perspectives *may* be wrong
My interest in the subject began many years ago when I lost a loved one to a heart attack to which a high-fat, Atkins-type diet was almost certainly a contributory factor. (This individual came from an exceptionally long-lived family, but died at 64 after being the only member of that family to switch to a high-fat diet. Neither the individual nor other family members had high sugar intakes.) Since then I've seen friends, colleagues and even family suffer from heart- and gallbladder-related health issues, and in my experience it has always been the ones on high-fat diets (either Atkins-type or simply proportionally very high fat intake) who have been affected. Moreover, those affected have usually been able to control/improve their condition by switching to a low-fat diet. Again, high sugar intakes have not been apparent, although it is only fair to say that, without 24-hour supervision, it is possible that some individuals have ingested higher amounts of sugar than is evident to an onlooker.
This is, of course, in no way a scientific study, but simply my experience. There must be people who can eat substantial amounts of fat without doing themselves any serious harm, just as there are individuals who can eat diets high in sugar - perhaps their specific genes protect them from damage. No doubt science will give us the full story in due course, and it's unlikely to be a one-size-fits-all diet.
But meanwhile (with the NHS performing 60,000 gallbladder removal operations per annum, and 103,000 people in the UK suffering heart attacks each year, and 94,000 people dying of coronary heart disease annually in the UK) I, personally, think it highly inadvisable to risk a high-fat diet OR a high-sugar diet. And that's just my opinion, nothing more.
[Statistics from NHS and British Heart Foundation]