Is it possible to un-spoof a spoofed caller ID?

When a call is placed into the PSTN, three different numbers are associated with it.

1. The standard caller ID: this is analogous to reply-to: in an email. This can be anything the user desires, and the name is matched from an external database.
2. Calling ANI: This is the phone originating the call, it typically has to be a number on the caller's account.
3. Charge ANI: This is the number that will be charged for the call, or whose carrier will be reimbursed for a toll-free call. This number is always a number on the caller's account. (except in cases where it is empty, like skype free calls in the past)

Consider the case of an executive making a call without assistance.

Caller ID: +1 (123) 555-3102 - Secretary's number, who should handle return calls.

Calling ANI: +1 (123) 555-3112 - Executive's direct number, the number making the call.

Charge ANI: +1 (123) 555-3000 - Company's main call in number, the account that will be charged for the call.

However, only the Caller ID is sent to the end user, unless the call is toll-free, or the callee subscribes to ANI from their provider.

It is also worth noting that a user can dial a feature code to have the call 'traced', and diagnostic information retained, but a court order is required to access this information (and possibly ditermine the true source.) However the customer is charged for the trace even if no investigation is made by the authorities.