Question: What is a single word to convey the sense of "inaccurate suspicion," but that tends to infer a bit of unfairness, such as 

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> It is immoral to use brutal force in response to [inaccurate suspicion].
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Answer: 
Inaccurate suspicion is supposition, but, as commented below, I think **misconception** is closer in meaning to the above question which is dealing not with a prior, unvoiced, suspicion but is about a suspicion that becomes active - so misconception would then be more appropriate, I feel.

***Misconception***

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> A view or opinion that is incorrect because based on faulty thinking or understanding.‘public misconceptions about antibiotic use’
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[Oxford Dictionary](https://en.oxforddictionaries.com/definition/misconception)

> 
> supposition
>  ˌsʌpəˈzɪʃ(ə)n/Submit
>  noun
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> a belief held without proof or certain knowledge; an assumption or hypothesis.
>  "they were working on the supposition that his death was murder"
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[Google Dictionary](https://www.google.co.uk/search?q=supposition&oq=supposition&aqs=chrome..69i57j0l5.3036j0j8&sourceid=chrome&ie=UTF-8)
**bogey** noun (FEAR)

[ C usually singular ] (also bogie); (bogy)
something that causes fear among a lot of people, often without reason:
the bogey of unemployment

<https://dictionary.cambridge.org/dictionary/english/bogey>

"a mere bogey" gets the idea over even better but you wanted a single word.