The PCR thresholds are chosen to minimize false negatives, not false positives. A sample that required 30+ replication cycles is unlikely to come from a person

The PCR thresholds are chosen to minimize false negatives, not false positives. A sample that required 30+ replication cycles is unlikely to come from a person that is infected/infectious, yet it would be counted as "positive". The thresholds are derived from experiments under lab conditions, providing a safe lower bound. That does put into question the validity of counting PCR test positives as a benchmark of viral load among the population, but as a safety measure for potentially infected individuals, the trade-off is worthwhile.