Watch the beginning of the 1983 Michael Douglas movie, "Star Chamber." The first scenes show two men getting away with the rape and murder of a young boy, because the damning piece of evidence (a bloody shoe), was found in their van pursuant to a search in violation of the 4th amendment. The audience is supposed to be outraged by this failure of justice.
Surely you've heard the consternation about criminals "getting off on a technicality." A lot of people view procedural protections as just that: technicalities. It's people with that mindset reacting so negatively to this documentary. To them, Avery's actual guilt or innocence is the important thing. The process is just technicalities.
The same mindset makes it easy to justify police misconduct, and I imagine it was strongly at work with Avery's jury. Once you admit the evidence excluded in the documentary, such as Avery's prior conduct, it becomes quite reasonable to conclude that Avery is actually guilty. At the same time, with the "planted blood" theory seemingly debunked by the FBI test, the only blatantly obvious police misconduct you're left with is the planted key. If you view outcome as being more important than process, it's very easy to think of finding Avery innocent based on the planted key as simply letting him off on a "technicality."
[1] Not to mention the pervasive logical and legal fallacies in Ken Kratz's statements, which left me yelling at the TV.