IMHO the EFF have chosen the wrong case to fight here.
Therefore, if we made a rule that evidence that ties you to a crime scene (such as fingerprints) can be collected without a warrant, but evidence that identifies you as the perpetrator needs a warrant, couldn't the police simply collect the DNA from the chair without a warrant, and only use the DNA from that sample to tie him the crime scene?
Then, once he's tied to the crime scene, that could be used to justify a warrant to collect a direct DNA sample directly from him, and then they could use that second sample to identify him as the perpetrator?
And if the rapist in this case was questioned as a subject, the police could have gotten a warrant for the DNA anyway.
This typically happens with civil rights cases, and it's worth noting that there are certain legal groups that are better at it than others -- the Second Amendment Foundation is exceptional, and it's a large part of why their win record is so good.
If they're just comparing the DNA that was left behind at the police station to DNA they found at a crime scene, I don't see any issue.