Good observation. It looks like PCR is one of the most common method used to test for influenza:

"The polymerase chain reaction (PCR) assay is a rapid and sensitive method for detecting the

genetic material of influenza viruses, and is now the first-choice laboratory test for influenza

infection in both humans and animals" - https://www.who.int/influenza/gisrs_laboratory/final_who_pcr__meeting_report_aug_2011_en.pdf

"Diagnostic tests available for detection of influenza viruses in respiratory specimens include molecular assays (including rapid molecular assays, reverse transcription polymerase chain reaction (RT-PCR) and other nucleic acid amplification tests)" - https://www.cdc.gov/flu/professionals/diagnosis/overview-testing-methods.htm