Siri doesn't listen to through built-in microphone.

I have an iPhone 6 (ios 9.3.5) on which Siri & dictation do not listen through the built-in microphone. Video recording (either camera), voice memos, and phone calls all do work through the built-in microphone. Siri does however listen just fine through my car's blue-tooth mic.

After over two hours on the phone with various quite nice Apple people I'm told among other things that there are two microphones in the device which serve different applications, one for siri/dictation/video, the other for everything else, or one for siri/dictation, the other for everything else. Does anyone know how this works?

Troubleshooting steps that I've undertaken so far include resetting all the settings available in the settings menu (network, etc), turning features such as Siri and HeySiri on and off, and a complete reset of the phone through iTunes. None of these attempts have yielded any change in the device's behavior.

It was suggested that I just upgrade to the new iPhone 7 but after this runaround I'm reluctant to consider another iPhone until I have some clarity.