Recover User Data When Mac's Filevault2 Won't Boot

One of our Macbook Pros running Lion mysteriously stopped booting after a perfectly ordinary shutdown.

All of the advice online failed to help (such as trying Diskwarrior - which could not unlock the drive, running Disk Utility via the Recovery Partition, and even various adventures with Terminal, all of which indicated the System on the boot partition was corrupted).

The gist of advice online is that
(a) whatever is not backed up is lost, and
(b) a full erase/system install will be required.

Turns out that (a) was not true at all... if ("when") filevault corrupts your system, you can access/backup the user files via a different computer.

Removing the drive and plugging it into an external dock connected to another Macbook allowed full access to all User files. So we were able to copy all the files, erase the disk, then restore from an older backup, then replace the user files.