https://www.nbcnews.com/news/us-news/lawsuit-alleges-ex-harvard-medical-school-professor-used-sperm-secretl-rcna129696
Sarah Depoian's daughter conducted a home DNA test and discovered Dr. Merle Berger was her biological father, according to the lawsuit.
It may not be CSI quality, but it is FBI quality! Those EXACT tests and types of matches were how they identified the golden state killer and identify hundreds of John/Jane Does every year these days.
Turi King, who worked on the Richard III identification, has done very great and approachable lectures on those tests and how they're used in forensic genetics. Highly recommended watch BTW, and several are available on YouTube - she has one on just those tests and how they can be used as well as discussing their strengths and weaknesses with examples.
The "I'm 3.2% Native American" stuff is (mostly) BS, but if it's identifying specific matches, it's pretty strong evidence. It's not definitively HIM until they test him specifically, but it is the exact sort of thing that should put you on a suspect list and warrant him spitting in a cup, yeah.
The only way I could see it NOT being him is if he was using a close relative as the source, but I'm not sure why he wouldn't say that once challenged. Technically, that would have fulfilled the requirements of "anonymous" and "unknown to the mother" he promised.
It's not definitively HIM until they test him specifically
That's my point. They haven't identified him, the company said she matched some of his relatives. However, it's quite possible that she also matched some unrelated people, i.e. this is a false positive.
This is closely related to the "prosecutor's fallacy". If the doctor had only a one in a million probability of matching her DNA, most people would consider this conclusive evidence that he is the father. In reality, there are over 300 individuals in the US who would also match, so absent other evidence there is less than a 1 in 300 probability that he is the father.