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You're missing the point: the tests don't specify the virus at all.

PCR cannot do that.

The test is claimed to do what it cannot do. It is not a test for SARS-CoV-2. It just amplifies sequences. A test for a viral infection must detect a virus, which PCR is incapable of doing.

It's like claiming the DEQ tests detects cars. It doesn't do that at all, and using DEQ testing to prove it's being used on cars cannot prove it's being used on cars. The DEQ measures specific particulates in exhaust fumes, which can come from a variety of sources, such as trains, planes and automobiles.

Tests to detect viruses can be made, and the PCR test isn't one.