Speaking from a ArcGIS Server Administrator point of view, if the Rest Services Directory is disabled, it is most likely because they don't want others to use their services directly. This may be because of security reasons or due to their internal infrastructure not being able to handle a load from other apps. By default, it is not blocked, so it would have had to be set. Although there are ways you can sometime hack this info out of a service, I would highly recommend requesting permission from the service owner before using their service. (climbing down from my AGS Admin soapbox now)
If this is within your agency/office...I would talk to your AGS admin to see if there is a way to provide access.