I mean there are legitimate reasons to criticize that scene. Relying on stupidity is generally a writer crutch (although people are, in fact, stupid sometimes) and there might have been a better way to get out of that scene (if they removed the "are you HYDRA" question, it might have worked better because it didn't leave an obvious unanswered question, but the pacing would have been off). But I don't think whether or not Romanoff could have beat it was at all relevant.
However, in spite of criticisms of the scene, I thought that scene had a lot of positives. It gave good insight into each character. It showed each their reasons for being there. And it had a Doctor Who reference. I liked the mixed feelings I had with Ward almost getting caught (my instinct was "oh no, he's going to get caught," while my rational side said "wait a second, I want him to get caught, don't I?"). Given all this, the scene was a good edition to the episode and it needed some solution that didn't reveal the plot too early.