The study had no objective conclusions that support this article's claim.

The study didn't determine a causal relationship between sodium intake and quallty of life but
correlation between changing diet with the intent to reduce sodium and quality of life.

That difference is important  The study was not expecting to find the secondary effects, and was not designed to monitor or measure anything except sodium intake.

Sodium is not an isolated dietary component that is consumed independent of other dietary components. It is a flavoring and preservative ingredient with the highest amounts being found in commercial processed convenience and snack foods.  Many of these are unpalatable or unstable without salt, so other ingredients are substituted in "low sodium" versions, or other foods are chosen by the consumer.  

For participants to reduce sodium intake they had to choose to consume different foods. The most likely was substituting unprocessed or less processed components for popular commercially processed ones or eliminating some processed foods.

The simplest change would have been to eliminate salted snack foods which have high levels of salt, carbohydrates, and/or fate and sugar, with low levels of fiber.  The complexity of the ingredient changes in these foods would make it impossible to determine from the collected data. which ingredient change(s) produced the observed benefits.