While it is true that sugar causes inflammation (and it is really the metabolism of glucose that is inflammatory--so any digestible carbohydrate), saturated fat only contributes when eaten in conjunction with a lot of carbohydrate.
On a low-carb diet, saturated fat actually has anti-inflammatory properties.
With highly-processed foods, again, it's the carbohydrate/glucose/fructose.
Salt is "associated" with inflammatory diseases. But that's because research in the field of nutrition is so poor (but not due to incompetence) none of the associations they find are worth their salt--so to speak.
If you are interested in the problems with nutrition science, check this out:
And again, on a low-carb diet, you really need to use more salt on your food (or eat naturally saltier foods). The reason is that on a high-carb diet (like most people eat), all that glucose in your system holds onto water--so your body tissue (muscles, skin, etc.) get so full of water, your blood vessels can't expand like they should. If you go on a low-carb diet, you will use up a lot of that glucose--and the water it held will be released. BP normalizes, but all that water leaving your body takes the salt it was holding onto out of your body as well.
Maybe you are getting the sense of why a low-carb diet is so beneficial to humans!