Thanks for the link (impeccable source
It's another way to look at the sensitivity issue:
DNA from some potentially dangerous organism doesn't mean you're ill due to that organism (and/or virus - not sure how they're classified).
PCR tests are so sensitive they can pick up levels that are far too low to cause any problems.
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This might e.g. cause misuse of DNA data in criminal cases. For example anyone close to you on a train, bus, elevator, corridor, etc could leave some DNA on you or your clothing by brushing past you, or even by exhaling in the same space.
So if Law Enforcement is allowed to use "any amount of DNA on a victim" as justification for assuming the person is a genuine suspect (and e.g. detain, arrest, or formally interrogate them), "false positive" are inevitable.
Personally I've never voluntarily given a DNA sample for anything and never will (because some version of this has been inevitable for many years).
But for many medical services they take bio samples, and these all have some identifiable DNA in them. So it's become effectively impossible to avoid providing a reference sample.
FYI the computer tech to do things like this anonymously has been around for decades, and the infrastructure would be far cheaper than modern payment-card processing (you'd only need a tiny fraction f the number of endpoints).
Sadly nobody cares about this except IT people (who understand the risks and the ways to resolve them), and it's not going to become politically relevant any time soon.