By the time the hawk- or "Agent Clint Barton" as he had introduced himself, had contacted her, Natasha had already grown tired of the lies that the Black Widow Ops program was telling. She knew that the memories planted in her head were false but to her extreme frustration she simply couldn't find any but them in her mind. There was nothing but what the Red Room had given her.
She growled as it hit her again how she had lost everything, including herself through their training and she thought about the S.H.I.E.L.D. agent's ultimatum. She could give up the only life she had known and leave with him to the United States, or she could be killed. Natasha had smiled when the archer added on the last part; he was no match for her on his own. Sure he was handy with his weapons; she had observed this in person after stumbling upon one of his targets, but she had better reflexes, she was better in a close fight, she had been engineered to be faster and stronger than any normal human.
So the choice was completely hers, she could stay and continue working for a cause she was no longer sure she stood for and maybe find out the truth of who she was, or she could leave and see what S.H.I. . was all about. "Pick which side you're on Romanoff." She thought to herself, "You're running out of time." Agent Barton would return that night to hear her final decision, but if needed she could be long gone by then. She had disappearing without a trace down to an art.
By the time nightfall came around Natasha had made up her mind and she was ready to execute her plan. "You're giving up a lot" she mused. Yet at the same time there was too much to gain to choose the other path. A shadow appeared and the hawk appeared out of the darkness as he proceeded to look at her expectantly. "I expect you've decided?" He asked, his piercing eyes analyzing her and the room around them planning out a method of attack.
The spy smirked. "Of course I have. And I see you don't expect the answer that you want to hear."
Clint frowned in response, pausing before asking, "So, whose side are you on?"
"Right now? Nobody's. But I'm done here, so let's get out of here."
And they did.