It’s not that hard to copy DNA. So it’s not clear how a DNA fingerprint would prevent counterfeiting.
The DNA mark is a hash of several thousand DNA strands, ONE of which is the authenticator, which is determined by a polymerase chain reaction analysis that is very specific to the target DNA and blind to the others. You could possibly include two targets.
A counterfeiter can indeed retrieve all the DNA strands, but would have to copy all of them, the chaff and the target, to succeed. They would not know which is the target strand. This would take quite a while.
The US supplier, though, just needs to add a known strand to the existing hash.
They use this technology in the UK in the dye packs that banks slip to robbers. Each dye mark can be traced to a specific bank.