I had the exact same problem.
I tested on two sets of iPhones paired to their own Apple Watch.
I tested this with my own app I'm developing and a one I downloaded from the App Store that uses the Audio Recorder Controller in watchOS 2.
My own personal watch worked but my work watch was not picking up audio despite displaying the audio recorder. It was just recording blank sound. This was true for both my app and the downloaded 3rd party app (RecorderHQ Free).
What I did to fix the problem was to reset the watch. I went to the Watch app on the iPhone and then went to Reset All Content and Settings in the General section.
After doing this, it all worked!
Hope this helps!