If you take a "third world dump", your lower back has to round.
After all, you should be able to relax.
Exercising is a different thing altogether.
Depending on genetics, you can go very deep without losing arch. Some might even go ass-to-grass without losing tonus.
You have to understand that while an unloaded spine can happily go tail-under, for the sake of exercise, you rather don't want to lose tone, especially with an exercise such as the free squat, where you can potentially do hundreds of repetitions.
An oversimplification: This of doing pushups this way; you go down until your body rest for a split second on the ground, then you press up. Awkward, right?
If you want to rep out deep bodyweight squats, I'd say go as deep as your knees permit you to.
Although, on second thought, it is more complex like most things, if you want to truly grasp it.
Since I'm not an author here and don't plan to, let's keep it short and just say:
Experiment with both bodyweight squats ATG and squats to parallel/a bit below parallel, depending what suits you naturally, although it's normal that the range below parallel increases with practise.
the term thirld world squat is misleading and shouldn't be used.
It implies that there is a more advanced and/or civilized method.
Quite the opposite, actually, as everyone would benefit of enjoying full range of motion while [free] squatting and being able to rest comfortably in the deep-squat position.
It's basically a natural skill most western people have lost.
Some even say defecating in the relaxed, deep squat position provides numerous health benefits.