Here's the link to the scientific study:
https://onlinelibrary.wiley.com/doi/abs/10.1111/1556-4029.14038.
I checked and Wiley is the distributor of the very legit Journal of Forensic Sciences. They're saying that they were able to isolate individual cells from both the suspected killer, Aaron Kosminski, and a victim. The scarf was apparently the only known surviving item from the time.
It should be noted that this is almost certainly only possible due to home DNA tests and consenting to allowing companies like 23 and Me and Ancestry trace your genetic heritage for you. They have to have the single largest database of DNA and lineages in the history of mankind. That database is used by the police to track crimes so it can be used for this without violating the privacy notice.
Also, to counter the "DNA that old can't be reliable" argument.. unprotected DNA takes 500+ years to start degrading and, because of DNA's halflife, will take about a million to six million years to be undetectable. It is unusable around a million years old. We know this because we've sequenced DNA that old already and from multiple populations. It's also why a mosquito fossilized in amber cannot possibly have dinosaur DNA.