I don't maintain a tight grip. The only time I'm gripping is on the drop about the time the bell hits chest level. Then I lock my thumb over my index finger (think reverse hook grip).
In my fast videos it is hard to see what my hand is doing. I've also got small hands and they are not easily seen in those videos.
The videos on Youtube (my channel), I'm doing 25rpm. That's fast. My fingers are loose and may be around the bell (although now I tend to not even do that., but they are not gripping. In fact, the bell lands overhead on my hand so that I don't even have to grip it to hold it there. The bell has to land on the heal of the palm to do this. But, if you do this, you can rest overhead with a relaxed wrist. But, it has to be on the heal of the palm.
When the bell goes between your legs, the arm should be straight. The hand pointed at about 45 degrees. If the arm is not straight when it swings back, the bell tends to move in the hands and this causes callous tears.
Watch Valery's youtube Videos on the American Kettlebell Club channel.
The other issue is that you need to follow the bell. If you drop the bell and don't move with it, hand issues can occur because your hand is absorbing more of the drop.
Now, if you are new to snatching, there is acclimation if you didn't have callouses under your index fingers before.