The main advantage of having the root filesystem under LVM is that you can easily migrate your root filesystem to a new hard drive once you've added it to the volume group.
However, having the root filesystem under LVM creates new modes of failure that are extremely difficult to recover from...
The scenario quoted by the author, a corrupted filesystem, can be handled through an Ubuntu Live CD as it supports LVM and you will be able to fix broken filesystems.
A more catastrophic failure would be if the volume group itself became corrupted. How would you go about fixing a filesystem in a VG when the VG itself can't be activated? The answer is: with extreme difficulty, if it's possible at all.
My recommendations would be :
1) avoid using LVM for the root filesystem (recovery==easy),
2) if root is under LVM, don't let that VG span multiple disk devices (recovery==hard), and
3) if the VG *does* have multiple devices, don't let the logical volume with the root filesystem span more than one device (recovery==extremely difficult, but still possible).
Violate all three of these recommendations, and you're stuck doing a sector-by-sector forensic reconstruction to get your data back.