OK I've worked out the answer to my question. @minibois thanks for your assistance as it helped me in reaching this conclusion.
Basically I had to import the footage from my camera first, then accept the option for Resolve to auto-calibrate the video format to my project:
Then, I imported the intro. Now they both have audio
So, in a nutshell - if the audio from a specific source won't work, try importing clips from the source which doesn't work before anything else, to let Resolve calibrate itself properly.