I have applied wainscotting directly on drywall with construction glue for permanence, temporarily held in place with finishing nails. For this, the wall was drywall paneling, that was mudded and smoothly finished.
Sometimes the substrate panel is part of the finish, and additional trim is attached on top, for depth. It appears as an insert, but is actually painted backing.
I have also applied wainscotting on furring, in order to better align and straighten the finishing on walls with an uneven surface due to bulging of the drywall or rough unevenness of concrete foundation walls.
If you give yourself a backing, at a minimum some strips of plywood, you'll separate the rough work stage to provide support from the more fine work of aligning and patterning. If you find you need lots of strips to support staggered and small panels, a whole sheet might save you lots of work and provide the flexibility to make the task easier.
Always remember when watching youtube videos, that professionals fundamentally work differently from DIYers: it's all a tradeoff between cost, time & pace, skill and whether it's for a paying customer or a critical spouse.