Sound playback mutes in particular clip files after importing another clip file

Just starting with Premiere and getting some really annoyingly weird behavior. I have a bunch of .mov files and when I imported all of them, although the waveforms did appear in the clip viewer, they were totally silent when played back. I tried the bars+tone tester clip and that clip played its audio perfectly fine, so it is not an issue with my computer's audio setup, nor is it an issue with my computer's audio playing nicely with Premiere's.

After a while I experimented with importing one file at a time. The first file I imported, the playback had audio perfectly fine. Weird. So I import another file, and - lo - the FIRST file's audio playback went completely muted, but the second file's audio worked fine. Again, all the waveforms were healthy. After importing a third file, the second file's audio became muted and the third file's audio worked fine.

What on earth?