I would use a random computer for an emergency. Imagine something like a foreign country where the only/best means of communication is the Internet.

Anyway, I am "the guy" in the family who must know passwords, not only my passwords. For example, over the past ten years at least ten times, I've received a call from a house security company who was about to send the cops over to one of my relatives' house. I knew the password every time and prevented the cops from showing up. (I knew they were not intrusions.) I have been the only one who ever remembered the passwords because of my system for recalling. And, by the way, around me, the cops have the right to bust into the home if they get a call from a security company. That can easily end all bad.

So, about knowing passwords, I'm talking about the entire universe of passwords (including house security, padlocks, safes, etc) that I like to keep in my brain for quick recall. The security vault software is a backup.