I'm trying to figure out how an accidental transfer could occur in regards to the defense's own emphasis above on "an investigation that spans hundreds of members of law enforcement and apparently at least one lab."
As stated by defense themselves in the above document, on Nov 20 the ISP lab located the DNA on the sheath and performed STR analysis. At that point as of Nov 20, the DNA information from that sheath is now in the official system--no one can come and accidentally or deliberately put BK's DNA on that sheath.
So, that leaves us with before those test results were processed and in the system. The only recorded interaction between BK and a member of Idaho law enforcement was on August 21 during his stop for not wearing a seat belt by Latah County Sheriff Deputy Corporal Duke. There is no written report for that stop, and a request for body cam footage from that encounter was denied (this statement comes from about half way down in this article
https://www.tri-cityherald.com/news/state/article275083811.html, and no I'm not confusing it with the Oct 14 WSU stop), so we don't know what physical interaction if any occurred.
If there is the smallest chance that somehow that CPL Duke somehow got BK DNA on his/her hands from perhaps handling BK's driver's license, I'm sure it could easily be verified whether or not that officer was present at the processing of the crime scene and the evidence. Though that would assume CPL Duke then transferred that DNA from their hands to their uniform shortly after the stop and it somehow stayed there until they were present at the crime scene and in the vicinity of the sheath. But it only transferred into the snap of sheath, not the broader flat surfaces.
Or we could say that after CPL Duke theoretically got BK's DNA on their hands from his driver's license, Duke immediately came in direct contact with an item of evidence at a crime scene and transferred BK's DNA to it. This item was then taken to the Meridian, ID ISP lab for processing. And that tiny bit of now twice transferred BK touch DNA is transferred a third time to a work surface/piece of equipment in that lab and evades cleaning until the lab receives the knife sheath and begins checking it for DNA. Then it transfers a fourth time to the clasp of the sheath.
I can't think of any other way in which a member of ISP could be connected to accidental transfer of BK touch DNA. Washington state law enforcement would have had no direct involvement at that point, right? According to the PCA, WSU police didn't even come up with BK's name/auto until Nov 29th. The WSU officer who stopped him for the intersection stuff wouldn't have any means of transferring DNA from that encounter to the ISP lab.