I wouldn't exactly say they stole them. Greek mythology and Gods were in Italy before the Romans. There were Greek colonies in Italy long before the Roman empire ( The Romans often referred to southern Italy as Magna Graecia (Greater Greece)) and these colonies interacted with the Etruscans. Neapolis (Naples) Syracuse, Tarentum (Tarento), Rhegion (Reggio), Croton ( Crotone) are just a few of many Greek colonies in Italy. The nature of the gods changed and developed over time to the greeks. Appollo ( as an example) to a mycenean would have been different in many ways to the one worshipped in later hellenistic greece. In Homeric times he wasn't associated with the sun in the way he was later. We can hardly be surprised then if the understanding of the nature of the gods in Italy also changed over time. The Romans also collected Gods and similar ones merged together.