In a folder, under Pipeline Model Definition, you can enter the details for accessing a Docker registry.
Since I'm using private repositories on Docker Hub, I don't need to change the default Docker Registry URL (the help text says it "May be left blank to use the public DockerHub registry") — I should only need to set the correct Registry Credentials.
However, if you only set the Registry Credentials, they are not used during a build — the "https://index.docker.io/v1/" URL has to be explicitly entered in order to apply the credentials using a build.
It looks like this is where the logic is:
https://github.com/jenkinsci/pipeline-model-definition-plugin/blob/472688704e/pipeline-model-definition/src/main/resources/org/jenkinsci/plugins/pipeline/modeldefinition/agent/impl/AbstractDockerPipelineScript.groovy#L61-L68