EDIT: ...or another persons DNA. Note that in general you aren't sequencing against a desired match, but generating a target for some future sequence (obtained from a suspect) to match against.
PCR can make things up when it goes wrong, which can be as easy as getting the acidity wrong (acidity will cut DNA, which will then recombine into new sequences randomly, so will UV light. Both of these factors, you can bet your firstborn, were present in the sample). PCR (the kind used for sequencing, not the kind used for identification of viruses) does not fail when it is not given DNA or when it's given somehow bad DNA, as everyone in a microbiology lab has probably experienced, it just makes things up. If there is any DNA in the sample to trigger PCR to start, it will "finish". Just ... potentially with a lot of made up endings.
Given what exactly DNA is, and how this was collected, the odds of errors external to the testing procedure itself is pretty damn high (tiny sample, contaminated by loads of frankly incompetent people (police, whatever else you think of them, can seriously improve handling of samples. I'm not even arguing foul play here), contaminated/partially eaten by bacteria, irradiated by UV (which first mutates, then destroys DNA faster than you can say skin cancer), then this was inserted into a database with millions of samples.
Oh, and labs have a financial incentive to make this evidence stick.
Then the output: sequences are a LOT of high probability guesses (millions). So you will never have a 100% match between a sequence, as in a string, and a sequence you found. The output of gene sequencing is not the full genome, but a large amount of short sequences that don't quite fit, but almost, where an algorithm then extracts what might be called "globbing pattern" (if DNA is AGCCAGCAATA, the match might be AG?CA*AAGA (note the mistake at the end T->G). Yes, this is exaggerated, and yes, there's no '*', there's a special marker for "up to X letters missing here", where X can vary).
Important: these patterns contain mistakes. There are ZERO actual DNA sequences that match the output of sequencing. That's where probability comes in.
You do not get the actual sequence (although a "highest probability" match without ? and * can be produced, with the very important caveat that it's a guess with not all that high a probability. That's why they probably matched by matching the "globbing patterns" from samples in the database vs the evidence and then selecting the highest number of matches, rather than comparing an actual DNA "string").
One very relevant question to ask is "what was the probability of this match and what was the probability of the second best match?" (because it's going to be something like ~85% for best match and 75 or more for second best match, and there will be 100+ 20% matches)
And then there's the statistics problem. The police will focus on the odds that THIS match, BY ITSELF, happened. But this is not one match! This is the outcome of millions of matches! The vast majority were negative matches, and then a few hundred/thousand partial matches. That's how the misdirection works. The correct question to ask is "what are the odds, given a true negative rate, of a match if there shouldn't be a match?".
Why? Let's calculate: true negative rate 99.999%, a million people in the database. Odds of a false positive? 1-(99.999% ^ 1000000).
The odds of them fingering a random suspect when there is no positive match is thus: 99.99546023401903%.
As you can see, the more people in the DNA database, the less you can trust the results. Of course, you cannot, honestly, sidestep this problem by checking 10 databases.
This DNA match can be a starting point for an investigation. It is not valid evidence, despite the reputation DNA has. But you can bet anything the prosecutor will attempt to use DNA evidence as the word of God in a trial.
And where there is no question about at all, is that the police used people's DNA (not the murderer's) for something those people have never given permission for.
Also your details about error rates in sequencing aren't correct either (you often get completely accurate reads of reasonable lengths).