Is this phrase part of wider diving vocabulary or just something he came up with?
I haven't heard that particular phrase applied to diving, but I am not altogether surprised to hear it used. The concept is certainly part of the wider diving lexicon. I have seen duct tape used on scooter housings, drysuit neck and wrist seals, drysuits themselves, wetsuits, fins (and fin straps), BCDs, LP regulator hoses, etc. If there was ever a scuba equivalent of the Red Green Show, I am sure duct tape would take its rightful place in many episodes.
And, although I think the term 'careworn' is a descriptor most aptly applied to people, some of the adjectives that appear in most dictionary definitions of 'careworn' - 'sad', 'tired', etc. - could easily be applied to gear.
I won't say that I am, or have been, a regular duct tape diver but I have used duct tape for several of the applications mentioned above (not the regulator hose, though). A roll of duct tape goes with me in my save-a-dive box. And, I confess, just like the Deets character in Lonesome Dive, er, Dove, as a diver I 'ain't one to give up on a garment just cause it's showing its age”.