Here in the 516 part of NYNEXLand, the telco voicemail works exactly
as you described. There's one additional catch. If you three-way
call FROM YOUR OWN PHONE into the voicemail server, the server does
not receive the CID or ANI information from you, and asks you to enter
your mailbox number.
On a semi-related note, I have a Visa card from First USA Bank in
Philadelphia. When dialing in for customer service, the voice response
system only asks me to touch-tone in the last four digits of my
account number for verification (it has already done an account lookup
based on the incoming ANI). When I received a new card from them, they
sent what the industry calls a "dead plastic". It's not "live" until
you call the number on the sticker on the card and verify that you
received it. The sticker on the card emphasizes that you only activate
your new card "FROM YOUR OWN PHONE", as it does the same verification.
How is this related, you ask? When I was on a call telling a friend
about this, I tried to three-way into First USA's 800 number (800-955-9900)
and it acted as if it didn't receive the ANI information ("Please enter your
16-digit account number").
I wonder why that is?
11. NYNEX Voice Mail