JENKINS-34674 was not completely correct.
DEFAULT_SITE_ID has too wide effect.
- Jenkins uses another update site as a default one
- Jenkins renames the default update site to DEFAULT_SITE_ID
- Jenkins still uses this update site as a default, because it's the first in the list
Workaround: When adding an custom UpdateSite in the code, delete the default site from the list, rename default site to the original ID, then add it back.