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?