If a machine in a multi-machine site cannot reach the shared config-store location, requests directed to unsecured services on that machine requires a token in ArcGIS 10.2.2 for Server.
This issue is non-reproducible in ArcGIS Server 10.4 and later with the introduction of 'read-only' mode for a site configuration. This creates a local copy of the config-store for each machine in the site and removes the dependency of a single shared config-store directory.