I have trouble thinking that even the most monopolistic of companies today would put in the effort to collect the DNA of literally everybody by finding strands of hair or the like. If you you send it to them, though, that's another story.
Google drove cars taking pictures of every street around the world and even sent people with camera backpacks up mountains and the like.
It's not hard to imagine them doing something similar with DNA, beginning in public spaces like restaurants and coffee shops, before pursuing further out nodes on the graph.
Streetview information is public, your dna is not, google would get sued out into oblivion if they did this.
Aren't the hair strands and fingerprints you leave on public surfaces also public, just like any part of your private property that happens to be visible from the street?
Physical access vs. Internet access - two very different things.
There's a big difference in obtaining someone's hair vs people paying to give you their dna.