Ketchup contains mostly tomatoes which naturally contain oxylic acid.
The ferric oxide (rust) formed on metal surfaces is basic in nature. The acids in Ketchup neutralise the basic oxide.

Table salt and white vinegar make a decent rust remover. That's because the molecules rearrange in solution to hydrochloric acid and sodium acetate.
Ferric oxide (rust) is soluble in weak hydrochloric acid solutions.

Salt alone, or in a paste in water works to remove rust as a simple mild abrasive, but only on a mechanical level.