This translation is a bit inconsistent. The original sentence says "She eats salsa", but the vocabulary and the other sentences translate the Spanish word 'salsa' as 'sauce'.

It is not English, even when salsa is replaced by sauce. I would change the sentence to the more meaningful Ella cocina salsa

Why isn't it good to say with 'eat'? How would you say 'She eats sauce.' in Spanish?

The translation is technically correct, except that we usually eat something with a sauce. Therefore I would Say "Yo como un pollo con salsa".