Depends what you call off road. My trekking bike is often used on paths like this:
View attachment 23676
....
It wouldn't cope with any seriously muddy paths.
I have taken my road bike down worse than that first photo albeit slowly.... (2nd, 3rd & 4th pictures down in
this link). But I would not consider the video with panniers on the road bike. The photo looks fine to me if you are careful - road bike & panniers...
As for the video link - our expedition bikes & our mountain bikes full laden have been over much worse at similar speeds - and that's why they are 26" mtb wheels.
However, I when I refered to "remoter places" in the context above, it was in reference to places like the very far north of Norway at the Russian/Norwegain border with the Barent's sea - a seasonal road open 5 months a year, Eastern Europe & Russia and the bikes were purchased for the sole purpose of handling roads such as the Pamir highway and going out through the border along Chile/Argentina (that illgeal jungle route) that we never made it to.
However I can come up with plenty of places in the UK that it is perfectly legal to cycle and tour, but you have to have a certain madness about you (

) to even want to take an unladen bike with you and not one of those places I would want to consider anything other a 26" bike designed for those conditions - and I still remember having to carry my bike for several hours to negitoiate certain 'hazzards' that were difficult enough underfoot (hiking boots) without the bikes & kit!