No, I understand (they caught a killer in Italy in a similar way, though in that case the dna tests were taken after the fact, in a sort of "gradient ascent" pattern).

But your example is that of a licit, even desirable use of those dna tests. They can be used for bad purposes, but that is what you have a government for: to decide what can be done and what can't. Health insurances obtaining your dna sequence from a third party to change your premium? Abso-fucking-lutely unacceptable. (And besides, at that point, what keeps the insurance company from asking your dna directly, unless you want to pay max price?). If you can't keep the government from allowing such things, you should either campaign to change the government or emigrate. This whole "let's keep a profile as low as possible because the government might go against me someday" is both a bit paranoid and fatalistic. If you distrust the government so much then you should put all your energies in changing it, not in keeping a low profile.