Written authorization takes ten seconds to write, and 60 seconds to fax to you. It may take a little longer to get someone to agree to grant it. If they're unable to obtain it for you, stay out of their system; they apparently don't need your input badly enough to offer you assurance that you won't be sued for providing this help.

If it looks like this question is going to come up again, why not proactively talk to the decision-maker to offer your services as an outside consultant. You could pre-arrange any paperwork that would make both parties feel more comfortable with the agreement. Everything would be out on the table ahead of time. You would still want per-incident authorization, but if the decision-maker preapproved your arrangement, per-incient authorization could be pushed down to a person of lower level, where the big boss wouldn't have to be awakened at 3:00am every time you are needed.

If, upon attempting to pre-arrange such an agreement, you find that you meet with resistance, you'll know ahead of time that you're definitely not authorized to access the system, and so will those people who keep asking you for help. On the other hand, if the decision-maker approves of the idea, once again, you and your contact within the company will know ahead of time that your involvement has been blessed.