Thanks for your response. I was under the impression that the UID of a user within a container matches that which it runs under in the host machine. It sounds like that is not the case.
From what I've read, the user running a container really starts to matter when the container is given access to the filesystem (using a volume). It sounds like the user within the container still wouldn't matter in this situation, but the user running the container on the host system would have to have appropriate permissions to the volume.