Indeed. The problem is you set up a false premise. The Police did investigate the Zimmerman shooting.
Yeah, but you see? You can't convince a conspiracy theorist that the police did their jobs, because police are always experts and incriminating any saint that crosses paths with them, so obviously if a person's isn't found guilty, it's false investigation.
They interviewed him, and found his story credible.
Which is what we're told in the liberty movement NEVER to believe. The police never believe what people say and they always do the wrong thing, if they arrest somebody, he's innocent, if they don't, he's guilty.
They examined the physical evidence, which was consistent with Zimmerman's testimony. They interviewed neighbors, most of whom were unhelpful but to the extent they could add anything, they tended to corroborate what Zimmerman said. Having no evidence that a crime was committed, the police made no arrests. That doesn't mean if evidence does turn up later they won't reconsider that position. But for now they have no cause to move forward. If you found yourself in your hypothetical alleyway situation, you'd be treated exactly the same.
or as a conspiracy theorist would say "they said they did it".