There is absolutely nothing incorrect about forming a fist as you describe in paragraph 2.
If I fold my fingers naturally, the tips of my fingers reach approximately 1 cm below the finger-palm line (the green line in your photo). I have never injured my fingers in over 2 decades of hitting heavy bags.
In fact, if your fingers naturally curl to this point, it will probably be impossible for you to curl your fingers correctly and keep them above the line.
When you form the proper fist, the tips of your fingers will likely be pressed into the middle of your palm.
The most important aspects of the fist are:
- It is as compact (free from voids) as possible,
- The bones of the top of the fist are parallel with the bones of the forearm, and
- The thumb is curled around the middle phalanxes of your first two fingers (The thumb will likely reach only to the centre of the second finger, closer to the second knuckle).
As you probably know very well - and as most coaches point out during a student's first lesson - the thumb should never be kept inside the fingers.
The fact you experience no discomfort when punching using a fist as you describe is a good indication that your fist is adequate. It is very difficult to execute a powerful strike using a poor fist without experiencing discomfort/pain/injury.