There was a rumor swirling, and I don't know if it's true, that they wanted the name "Folsom" in the bridge because, goodness, we wouldn't want Granite Bay to try to claim they had a part in building it, or any other surrounding community that uses the bridge for that matter. They wanted to make sure Folsom got all the credit (and by extension the City Council).
I hope I'm wrong about that, but I seem to recall that being a factor in the decision that was mentioned. Maybe someone in the know can set me straight if I'm remembering it incorrectly.
I think you're correct that they wanted "Folsom" in the name, which I understand. They didn't want the word "Dam" in the name because they also didn't want the Bureau of Reclamation to get credit. So I guess there was some ego involved there, because heaven knows Folsom Dam Bridge wouldn't have made as much sense as Folsom Lake Crossing.