It seems it is the carbs and added sugars, found in processed foods, contribute to heart disease, more so than salt.
"Ingesting one 24-ounce soft drink has been shown to cause an average maximum increase in blood pressure of 15/9 mm Hg and heart rate of 9 bpm. Those who consume 25% or more calories from added sugar have an almost threefold increased risk of death due to cardiovascular disease, according to the research." - Medical News Today
The biggest offender? High fructose corn syrup.
Most natural sugars have a balance of fructose and glucose. They are beneficial in fruits and vegetables. However, high fructose corn syrup is not balanced, which can lead to acidic blood, damaging the lining of the veins.