I think you're missing the forest for the trees for here. It may technically be a pull, but the thought process involved is most typically "I want to send my code over to _____".
Unfortunately git is to powerful to handle its UX like that. Users have to understand the model behind it. If you have ever tried to work with teammates, who did not fully get yet how git works, you know what world of pain that is. They have to think like git works, you cannot abstract this away into their understanding of SCM.
