If I understand the service you are describing correctly it is that of ID protection rather than the service outlined by go daddy which is coined Ownership Protection which simply involves locking the transfer or modification of the domain as long as the domain is set to auto renew.
ID Protection simply replaces the users details with that of their providers details and an email address, such that messages are passed to the domain owner via their provider, said email will change upto 7 times a year to avoid spam.
If this is the service your are trying to bypass, there are two approaches:
- If ID protection is not purchased with the domain often the records can be acquired via sites such as domaintools who store historical WHOIS data (fee involved).
- The alternative is to contact the provider directly, however unless the issue is that of a legal nature I would doubt many providers would provide any details.