I think the ambiguity comes from the poor way it was handled; the fact that she called herself a monster directly after revealing her sterilization - along with her taking on a motherly role in the film regarding Hulk (she's the only one who can calm him with a "lullaby") and the "Aunt Natasha" moments, as well as some oneliners ("I'm always picking up after you boys") - I can easily see how it can be interpreted as such. I don't believe this facet of her monstrosity was intentional or at least as intentionally stressed by Whedon as it comes off, but it's definitely important to point it out and criticize it for what it is.
Yes. It's totally fair to point it out and criticize it, but I don't think it's necessarily true either.
To me, I look at that scene with Natasha as a person who was raised to be a killing machine - an implement meant only to cause pain and suffering. All she does is take away life, she can no longer give it. I think it's a very powerful message, myself. I did buy that Natasha sees herself as a monster - many of the characters call themselves monsters in this movie. A lot of people are hard on themselves and are figurative monsters where the Hulk is a literal one. Natasha can also be a case for a literal monster as well, but she has a lot of redeeming qualities, I think. Could the writing have been a bit tighter? Sure. The issue definitely comes from the order of the information given, without a doubt. I do think it's just... ignorant... to assume that "because this was the last thing she said, she is a monster solely because of no babbies". It's just a dumb way to approach scenes, but it's also important at the same time to realize that it's a way people can read into things.
I also think it's fair to criticize Natasha as the mother of the group because, even if it wasn't intended, she does come off that way in many scenes. I didn't think twice about the Auntie Nat or the "picking up after you boys" but I think it's a fair criticism. We're in a social climate right now where female characters are being heavily scrutinized. Especially in the Avengers where a large majority of your main characters are white males and the token female. You're basically asking for huge amounts of complains to be levied against you. No Black Widow merch on the shelves + iffy characterization = problems left and right.
Are they all fair? No. Are they all important? I think so. While I'm sure a lot of people don't really dislike ScarJo's character, it's okay to not be 100% satisfied with it. There's always room to improve, I think. I hope a lot of writers see what happened here with Black Widow and try to avoid the same pitfalls going forward.
No, Widow being captured is not Damsel in Distress because she engineered the morse code thinger and relayed a message to Hawkeye that helped the entire team find Ultron and set the stage for the final conflict. Without her, they may not have arrived in time to stop him. She busts herself out, she doesn't wait for someone to rescue her.
I'm all over the place, but these are my thoughts.