“The Black Widow is very cold, and rarely ever smiles. People know to avoid her, because everyone knows that she will kill you. Hawkeye is deadly from a distance, and everyone knows it, but down at street level he’s everyone’s buddy. Everybody lets Hawkeye sidle in close. And really, Natasha sometimes admits to herself, this is why Clint is the deadlier of the two of them.” [headcanon submitted by TheShadierTwin]
Black Widow already lifted the hammer once before, without really thinking about it—just trying to move some things around in the Avengers’ tower. The scene where she says “That’s not a question I need answered” is just her being polite, and a good liar.
There you go. None of the Avengers are perfect. They all suffer from what normal humans would have deal with when faced with traumatic events like saving the world. Yet, despite all of their diagnosed shortcomings, they're still heroes. I see it as if they can be heroes, then so can we.