The record
On March 24, 2016, a user describes Siri on their iPhone 6 Plus running iOS 9.3 acting as if the microphone were broken. Phone calls worked, Voice Control worked with Siri disabled, and Siri itself worked through a car's Bluetooth mic, but Home button activation only vibrated and showed the Siri screen without the usual tone. In a follow-up the poster narrowed the problem to Home button activation rather than Hey Siri, and asked for ideas. No fix was confirmed before the thread closed. It is a single report and should be read as such.
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A documented user report, not an independently reproduced test or an estimate of how often the problem occurs.