This part struck me as odd, too, especially when you consider the justification: That if you lose access to your sudo account/password, you must have some other way to get into the system.

Backups should include everything required to rebuild every server in the company. No server should be 'too critical' to wipe and start again if required. So maybe I'm being too much of an armchair warrior here, but the reason I don't like this one is less about the actual security implications, and more because of what it says about the fragility of the overall setup.