Not quite. That's probably what they told you in indoc, but it's not the whole story.

From the scheduling reference handbook (please read it early, read it often).

What If I Do Answer the Phone on an Off Day?

A pilot’s obligation to accept a trip on X days or regular line off days is not absolute, whether the trip is the result of a white slip (same day or next day), yellow slip, green slip, or inverse assignment. A variety of circumstances might make accepting such a trip impossible. For example:
• Not being physically located so as to be able to report.
• Having consumed alcohol.
• Lack of available child care.
• Lack of available transportation.
• Not being adequately rested. For example:
A pilot, not on call, notified of an inverse assignment should consider whether he is sufficiently rested and fit for duty to accept the scheduled rotation.
 A pilot is not required to accept an inverse assignment if he cannot meet the requirements of FAR 117.5 and certify fitness for duty for the assigned rotation.