My understanding is that it's not quite that simple. GANs have stability problems (and as a result somewhat out of favor atm) and if the fake detection mechanism isn't a differentiable function itself no training can happen.
What you need a a deep fake and a real video of the same thing, then train on the difference. Clearly this is impossible - which is what makes the problem hard.
The second way requires dramatically fewer update steps (usually) than the first. Thus - having your adversarial target be differentiable definitely helps, though it is possible to do even absent such a criterion.
Stable Diffusion produces faces- especially eyes that are malformed. You'll often see "restore faces" in online services which feeds the end result into a GFPGAN which is used to restore faces.