I have caller ID block enabled on my phone and my number shows up as anonymous or private caller. But when I call my dad's long term care facility the voice mail service reads my number to me as the callback number. How does it see my number if it's blocked? The number I dialed is a local number, not a toll-free one.
Not sure about this, but I would think that is because they fall under "Emergency Services". I don't think you can block your phone number from these services. Say you're having a medical emergency and call for help, but are unable to respond to their questions. Since they have your phone number, they can likely still locate you and send the appropriate assistance.