It is too long and complex to comment in detail without reading it all again. But St Augustine in City of God quotes at length Varro. Varro, a pagan itself, reputed as a leading authority on the pagan religion. But as far as I know his works survived only in quotations, nothing in full.
We should not apply our concept of revealed religion to them. For Christians, God came and revealed what we need to know for our salvation, besides supplying the means. Even if some details are confused in the mist of time and cultural translation, we may be sure that what we need to know to go to heaven is safe. For Catholics, it is not just the letter, is it the Bible+Tradition+Magisterium which support each other so that we do not need an intellectual miracle everyday in the mind of each interpreter, besides all the other miracles of life. What we need to know is there available to know when the responsible people do not screw it too much, and we always can go to other people or reliable authors. But pagans mostly do not believe in this way, with this certitude.
The pagan mythology that we know is a mix of ancient legends, theatrical plays, histories intended to be read aloud. It does not have an official interpreter or a cannon.
The pagan religion also mixes worship to the pantheon gods with worship to familiar gods and ancestors spirits. Their definition of family was not 'bloodline', was 'the ones who worship my ancestors'. (the famous Foustel de Coulanges book is another good reference)
A learned pagan could see that the plays and bard stories were man-made, and intended to entertain. He would known that some variations of the plays were newer than others. He also would see the contradiction about praying for justice to a god which transforms itself into animals to seduce women around.
Varro distinguishes various ways and reasons to believe, and he gives some nice names to them.
Yes, people could believe in the gods, even if they knew that some histories were man-made, entertainment, or just BS. They still could believe in the cosmology, or that they could pray to the gods, and believe in part of the mythology.
But even a more skeptical man, one who knew better the development of the mythology, one who really did not believe in any detail in any story, still could see other reasons to believe:
What else are they going to tell the people? What will keep the loyalty of the people if they do not pray to the city gods?
How are you going to cool the head of your crazed teenage son if you can not appeal to the spirits of the ancestors, the tribal gods, and the honor of the family name?
So Varro points out that there are a 'keep-order religion' (I don't remember the category names), and that a wise man should not mess with it if he wants some order in his city and his family. What Varro says is more or less: "Do you have some better idea? No? Then shut up."
Besides that, familiar gods and ancestors worship is a much more natural belief than stories about a pantheon of gods. It just requires a basic belief in immortality of soul and that there is someone above us.
The point is that both sides, pantheon and familiar are linked. It is hard to expect of them to believe only in one side.
First, a common theory for pantheon development: the main family god become the gens god when the family grew into a gens; then the main gens god become the tribe god; then the tribes gods were put together into a pantheon of city-state gods.
Even if the Romans could not see the beginning of this process, they still could see that allied or conquered states would integrate their pantheons. They could see that Roman gods were variations of Greek gods, the Roman themselves adopted gods from other peoples, etc. It is an extension of the concept of the family. 'allied states worship our gods, we worship their gods, then they are really allies'
So they did not really need to believe in every theatrical play about Zeus screwing another poor girl to be a pagan. Even because there were no authority to determine which play was 'canon' and the more learned could see new plays and new gods taken from somewhere else all the time.
They could have a general belief in ancestor worship and family honor which extends to tribe and city, in some kinds of god-entities above us which hear us, and that their worship binds us together, a humane sense of virtue and justice, and still be a pagan.
Probably, he could accept that some of the mythology might be true, he could see the wisdom in some of them, and at least he would not know anything better. He also has to answer his children when they come with 'were we come from?' 'who created the world', etc. What would you say to your children?
Roman/Greek paganism is not much different that any other paganism, like Africans or Native Americans, it is just that their mythologies are better recorded and quite extensive after centuries of theatrical plays and books in written form. They might have better philosophy than an African tribe, but this do not make a revealed religion. It would be probably wrong to assume many of them were totally atheist-materialist, as hard as to assume a totally atheist-materialist Apache.
At the end, what you propose is not contradictory and they knew it themselves. It is not a modern idea and Varro wrote about it.
They could be pagans in a very general sense, and still believe that the religion is needed to keep order.
If you are asking you probably know that one of the main arguments of the Christians against the persecutions is that they still would obey the state even if they did not worship the state gods. (see St Justinian) This would be totally strange for the pagan mind. But this appears strange to them just because they did not take their gods as seriously as we (or the Jews) do.
Why cant these guys mix their tribe god with ours?
So I recommend you to read The City of God and Foustel de Coulanges (La Cite Antique). Actually after reading them, it was not so fun to me to read Greek plays, because when you understand their mind you already know what they will do, and there is no weird surprises anymore. Specially because most often we already know the big end and the surprises were in smaller attitudes and deeds.