Well, 9-12" width is better than nothing but you'd want at least 2' to be really fairly sure of stopping most/all comers. In some cases you need even wider, e.g. those with "professional foxes" around who've perfected the art of making a living outta peoples' henhouses... but fortunately that doesn't apply to very many people.
It's not so much that predators don't understand "the concept of tunnelling" as it is that they tend not to back up and try further away if they're thwarted close to the fence. But they won't always start, or stay, RIGHT AGAINST the fence, hence the value of a somewhat wider apron than you suggest. In particular you want the apron to be either REALLY well secured to the ground, or the edge buried/inconspicous/etc... you do NOT want them to get the idea that it is moveable or has a flappy edge right next to them...
Good luck, have fun,
Pat