First off, I’d say there’s no “right way” to manage digital assets. While I think most of us would agree that a well-defined workflow of labeled media and duplication is ideal, unfortunately, it usually comes down to your DIT’s personal preference.
Secondly, I’d make the argument that if that’s how they roll, just do what you’re told. If they lose footage due to the practices they’ve implemented, that’s on them – not you.
Finally, the system I’ve always used is a label face-up/face-down approach. Face-up means empty/backed up, face-down means it hasn’t been duplicated yet. I’ve also added one additional layer of security to that, by marking labels with a grease pen before starting a shoot. Once the DIT has backed up the clips, he wipes the label clean.
I’m a unique blend of overachiever and procrastinator. I’ll do it all – later.