Giving someone "benefit of the doubt" suggests uncertainty as to the motive or intention.
If a kid knocks over an ugly vase, and the kid claims it was by accident, you could give the kid the benefit of the doubt, and accept the apology.
So what does it mean to give someone the benefit of the doubt? According to the Cambridge dictionary:
to believe something good about someone, rather than something bad, when you have the possibility of doing either
Say you're 35 and single, and at every family gathering you get recurring questions on your plans to get married. As tempting as it is to assume everyone is out to ruin your day and the old fogeys are showing their age by insinuating outdated social values, another way to interpret the situation is to give all of them the benefit of the doubt. Perhaps they asked because they care about you. Or it's just an easy conversation starter. They don't mean you any harm and didn't mean to hurt you.
In this situation, I would say colloquially: 她們不是故意的，別想太多, or, they didn't mean it that way, don't overthink it. Neither "寧縱勿枉" nor "無心之失" is appropriate here. The former sounds stiff and out of place as it has a connotation of legal speak. As for the latter, the focus is on "之失". You've already made up your mind that the person is at fault, just that it was a fault committed unintentionally.
Depending on the scenario in which you want to say "give benefit of the doubt" in Chinese, why not consider 疑中留情? I first came across this term via this forum. The examples provided in this other forum includes letting a student retake his final exam, as he claims that a family emergency resulted in him having to miss the exam at its originally scheduled time.
In English, to give someone the benefit of the doubt is to believe in their [good] intentions. The emphasis is on the good intention, not the perceived slight, and not the presumably offensive action. In my experience growing up in my Chinese household, the emphasis was always on the outcome, the action. Intention didn't matter. If I were to assume most traditional Chinese household was like this, then yes, giving the benefit of the doubt is a foreign concept. It mattered most what was done, the action.