And I won't even get into all of the books that were rewritten and heavily edited at the different councils... Oh yes there was more than one.
The inclusion of Revelations as I understand it was hotly contested. Many didn't want it included. But the Council of Nicea wasn't about canonizing the NT, but about unifying the Church as a whole.
The Church historian Eusebius was believed to be on friendly terms with Constantine, so we can't be sure how much bias there was in his accounts. This is an honest and fair thing to say. But in light of that, there is no reason to believe that Eusebius was dishonest either. Unless there are very good reasons to dismiss Eusebius' account of what happened at Nicea, then it is generally conceded that his account is accurate.
As I understand it, Constantine did listen at the council, and did offer ideas and suggestions, but not as the sole authority. He basically appointed himself as judge or speaker of the house, for the purpose of keeping order during the council. His main concern was order and peace rather than theological doctrine. This he largely left to the bishops.
We can get into a long discussion about Constantine if you wish.
Oh by the way-
With regard to the story of the store keeper and snooty customer, I think I understand the difference in our opinions. I interpreted it as a story of moral principle,(like one of Aesop's Fables) while you understood it in the context of business ethics. From your viewpoint, within that context, you would be correct. I think this is one of the differences that keep atheists and theists from understanding each other. Our perspectives are different, and so are our concerns.