Did some research on the internet, but didn't find an answer yet. Just people with similar problems.
I downloaded a program called MediaInfo to tell me what the properties are of the files that work and don't work.
First, here's the MJPEG that Premiere sees no audio for.
Second, here's an uncompressed 8 bit YUV AVI grab that Premiere reads the audio just fine. As far as I can tell, the audio specs are the same with each.