This is one of the most common misconceptions about the Romans, because they teach it like some fanatical mantra in the school system.
While it is true that the Romans adopted a number of aspects of the Greek polytheistic culture, you can find a similar spread of god types across a great many cultures in the Mediterranean. The Romans did not simply 'take' Greek gods. They developed them on their own, they borrowed from Etruscans, they borrowed from Phoenicians, the borrowed from Celts, they borrowed from Greeks, and undoubtedly there was a reciprocal borrowing from these cultures from indigenous Italic cultures.
The polytheism and god types is a widespread Mediterranean phenomenon and not so simply explained.