According to the book, she had pretty good idea of who he was. And there was no promise to make family legit, especially as a condition of their marriage. He just shared his thoughts with her. But before that, she said: "I love you. I don't care!"
No pity to my fingers, as always.
OK.

Kay was still shocked, still horrified. She said to her husband,
-What made her say all those things, Michael, what makes her believe that?
Michael shrugged.
-She’s hysterical.
Kay looked into his eyes.
-Michael, it’s not true, please say it’s not true.
Michael shook his head wearily.
-Of course it’s not. Just believe me, this one time I’m letting you ask about my affairs, and I’m giving you an answer. It is not true.
He had never been more convincing. He looked directly into her eyes. He was using all the mutual trust they had built up in their married life to make her believe him. And she could not doubt any longer. She smiled at him ruefully and came into his arms for a kiss.
-We both need a drink, - she said. She went into the kitchen for ice and while there heard the front door open. She went out of the kitchen and saw Clemenza, Neri and Rocco Lampone come in with the bodyguards. Michael had his back to her, but she moved so that she could see him in profile. At that moment Clemenza addressed her husband, greeting him formally.
"Don Michael," Clemenza said.
Kay could see how Michael stood to receive their homage. He reminded her of statues in Rome, statues of those Roman emperors of antiquity, who, by divine right, held the power of life and death over their fellow men. One hand was on his hip, the profile of his face showed a cold proud power, his body was carelessly, arrogantly at ease, weight resting on one foot slightly behind the other. The caporegimes stood before him. In that moment Kay knew that everything Connie had accused Michael of was true. She went back into the kitchen and wept.

Couldn't stop shorter than that. It's so brilliantly written!