Hmm, well, I didn't live in the region anymore, so I am not sure how it went from first-hand (I got some second-hand info though). Based on that my take is that there was some pressure for sure. You need to imagine a cold case got assigned, and people want to get this over with. At some point, I even saw my own mother on TV commenting on the story, how she wanted the case to be solved.
From the source, 15000 of 21500 people complied. It meant a lot of families (of men) could be excluded, narrowing the gap for the perpetrator (the police figured the perpetrator was from the region as he must have known the area).
I am one of these weird outliers. Not only did I not live in the region anymore, I am the only male still alive from that region who fit the profile (12+ male at time of crime, my father and uncle both passed away). Thing is, the family tree can go back multiple generations, including in ways you're not aware of. You might have a relative alive who you don't even know about. The other reason I'm an outlier is my family isn't originally from that region. Even though my family isn't originally from around that area, it might have helped, for the earlier mentioned reasons. Plus, I got myself off the list, too.
Its a bit twisting, how you know for sure you didn't commit a (rather serious) crime, but you cannot be sure about others, and if everyone says they didn't do it therefore don't want to cooperate the police cannot narrow down on a suspect. On top of that, my father and uncle were both alive at the time the crime was committed (my father was legally blind at that time though, couldn't even drive or walk alone).
So how did I eventually get tested? After initially there was no outcome from the samples of people who still lived in the region, the police announced they'd locate men who were 12+ at time of crime and who live elsewhere nowadays. This included me. I immediately called the hotline for an appointment to get it over with. At that time, our first born was only a few months old, and I wanted to get it over with. They (the police officer) understood this and she made an appointment with me. There were 2 police officers: a female who did the social aspects (talking), and a forensic male nerd. I spoke with them about the case even though I reported the stalking matter in a separate report to the police (because it might have been the same person as the perpetrator). They were as friendly as every police officer I met in my country (always reasonable and friendly, according to my experience). I was approx 15 y.o. when all of this happened.
As for anonymity, yes it was supposed to all remain anonymous. All the DNA samples were going to be destroyed when the case was closed. I'm not entirely sure when that is though, cause of higher court still have to rule.
Later on I learned NFI only test a very limited range of DNA, about 50 unique aspects. But in general, all of this increased my faith in this executive branch of the government. As always, YMMV.
With regards to your last remark: "The suspect must have had a reason to run, instead of just refusing the test" simply said, the shared theory is his feet got wet. They got DNA samples from his place. Then he got on national TV being sought a suspect, and someone in Spain recognized him. He never admitted the crimes, btw. He argued he found the body dead and put the body away in a nice way, even though his history as pedophile, as well as his DNA all over the place on the victim's underwear. He (or well, his defense) argued he was scared to talk to the police because of his history as pedophile. I don't know, got me quite angry cause it smelled like BS.