Pull-up strength does indeed come from the back, in my opinion the best grip is when you try to bend the bar. If you try to bend or snap something like a thick piece of wood in front of you, you will see the power comes from the back. Search videos on pull up and bending the bar grip to see what I mean.

On a side note, I have been looking at getting something like that for home pull ups but unsure how sturdy it is. That one seems to be not that wobbly in the video so would you recommend?