The PCR tests are extremely accurate:
https://ag.umass.edu/services/tick-borne-disease-diagnostics
I'm more worried about the pathogens they don't test for (or are unknown).
I couldn´t see at a quick look that they are testing for the Borrelia garinii and Borrelia afzelii bacterias which are the most common in Europe. Hope I was wrong. Did you see somewhere how old dead ticks can be, and still be tested? I saved one 6 years ago. Would be interesting to see if we carry the same infections.