Right now, she doesn't care. This entire experience has been so hard on both of them Natasha doesn't have the energy to protest the white knight act. She'll give him hell for it later.

Or she'll remember it as the one of times someone showed her they really truly cared about her on a level she never thought anyone could. Coulson had done it, hell even Barton's made a grand gesture or two but this is different.

He hardly knows her compared to the way Phil did and Clint does, and yet Steve walked into her own private definition of hell, and even after she seemed to sell him out he's....saving her.

That blows her mind.