But they didn't suspect him at all. They found their suspect first, then constructed a circumstantial case (a, b and c) against him.
At the very beginning of any police investigation, police don't - or at least aren't supposed to - start out suspecting anybody at all. They are given (or they collect) information which leads to suspicions: testimony by victims or other witnesses, surveillance video, credit card and phone records, fingerprints, blood or semen at the crime scene.
In this case, the police found one line of evidence - DNA from semen - that strongly suggested the crime was committed by one member of a family. They then used a number of other, independent types of evidence to narrow down that original list, and eventually to get a warrant to test their single best suspect's DNA. What is your preferred outcome here, that the police ignore the DNA information that they did have? Or that a warrant to test DNA be denied unless the police have already specifically considered and ruled out all seven billion other people on the planet? Should police not be allowed to investigate cases when their first (or only remaining) lead is DNA evidence?
This is dangerous shit and the police should get slapped for it. And the public needs to step up and make it clear to judges that we won't tolerate them rubber stamping bullshit warrants. Just because there was a happy ending this time doesn't mean that we aren't playing with fire. This guy came one lab mistake away from from having his life ruined.
The police presented a plausible case - not an airtight, conclusive case, but enough to be probable cause - to suspect that the individual at hand was involved in the crime at hand. On the strength of that limited but suggestive evidence, a judge granted a warrant allowing the police to test a DNA sample (not search a house, not seize a vehicle, not throw a man in jail) to rule in or out a match with the DNA they had from their crime scene.
As I noted in my original comment, I can see the potential for a slippery slope type of argument, but the system actually seems to have worked properly in this particular instance. I agree that the situation is vulnerable to errors--but that's true of any criminal trial. A lot of cases have turned on eyewitness testimony that later turns out to be mistaken (often demonstrated by DNA analysis, ironically); does that mean that police should not use witness descriptions to identify suspects to investigate?