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)
Suspicion is suspicion. Whether your suspicion is based on assumptions or not, it is always the feeling or belief that something may be possible or true.

You can't have a bad suspicion nor a good suspicion. What you suspect to be possible is really what is at stake here, whether good or bad. The suspicion itself, however, cannot inherently be bad or good, only the actual event.