Towards the end, you're absolutely right; they didn't believe in the Greek Pantheon. Towards the beginning, though, what do your studies show? 
Additionally, that non-Christian gods were worshiped and are currently worshiped in earnest should be enough to establish the main point being made.
Hey, ive just created an account to participe on the forums but this message about the romans is mine
well, at the beginning of the early roman ages, the absolute power (the kings wich were the first rulers of Rome) could do anything without any actions taken.
a way to justify their leadership and to more easily control the public became... the Gods.
they "invented" the roman gods and said they (the kings) were their children! this would mean to the ordinary public that they should in no way object to the rulers, that they should follow them blindly and Believe everything they uttered.
after a few decades this became generally accepted and some time later people didnt even know about the "start" of the Gods, they just thought the Gods were so real because of all the stories told in wich Gods walk the earth as if it would be the most normal thing out there.
some started to think "why doesnt God appear to me then?" well there were 2 simple answers:
1) im not worthy. Gods will only come to me when I make myself worthy. how could this be done? the rulers provided them with solutions like "join the army! give money! vote for..!(when democracy arrived this is) be a good civilian! follow the leaders! etc...
2) they already have but I just didnt notice. they could have appeared in the form of an ant, or a dog, or a bird in the air, or a family member acting weird... but how do I really get in touch with these Gods? (wich were said to be proven when f.e people saw 3 birds sitting on the same branch or something like that...) well, go to part 1) of the answers.. they had to become more "worthy"
so the Gods tale started to lead his own life in a way that even the emperors themselves believed it, as they were the higher authority, the only thing u could do would be to believe yourself..
some years later the philosophers/writers saw tru all these tales and started to (secretly) share it with others, in that way the more "poeta docti" people found out about the fake Gods and eventually they were only used as decoration in poems...and ofcourse the poor people still believed in them
and yep, you're right about the point this makes
hope you dont mind reading this long reply lol...
sincerely, Thomas.