I'm not sure there is any point in making a distinction, because while the DNA identifies him as the perpetrator, it also ties him to the crime scene.

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?

I agree that this makes the EFF look very bad. Persecuting rape is difficult enough as it is. I can't figure out any hypothetical example where this kind of identification testing could be abused without literally fabricating all sorts of additional evidence.

And if the rapist in this case was questioned as a subject, the police could have gotten a warrant for the DNA anyway.

You can't choose what cases will set precedence, and, once set, it is very difficult to "unset".

Lawyers can and do choose which cases will be set for precedent all the time. It's somewhat difficult to ensure that your case is the only one going after the said precedent at the right time, but just about any time a new law is passed that people object to, lawyers begin shopping for ideal candidates and then determining the best ways for them to break the law in the least damaging way, and in the best possible district to get the law deemed unconstitutional.

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.