You might be thinking of the way they tried to catch GSK, by uploading a fake profile that was actually his DNA from the scene. JMO, but I don't think that's how these forensic genealogy companies make comparisons currently. GEDMatch was acquired by a competitor of Parabon right after some court cases limited them to only seeing those profiles that had opted in, so IMO they started compiling a private proprietary database of volunteers that they now use to compare, and I don't think anyone gets notified if they match as a second, third or fourth cousin to a sample.
This article details more about it (worth a read):
The controversial company using DNA to sketch the faces of criminals
From that article, there is this info:
In the meantime, the US Department of Justice has issued interim guidelines to help police with their use of forensic genetic genealogy, permitting use of the technology only for serious violent crimes such as rape and murder, and only after other leads have been exhausted. Notably, the document specifies that suspects cannot be arrested on genealogy alone — conventional forensic genetics must be used to provide a conclusive match.
So the Delphi investigators may not be able to pursue this course of testing yet, legally.
As for familial DNA testing in criminal databases, it's not currently legal in Indiana.