We are a trusting team and don't do pull requests with our closed source repos either.

To avert chaos it's much better to have an orderly branching model in place e.g. feature branches! My fellow partners made us go all "git flow" last year and the result has been a really tidy and satisfying workflow:

http://nvie.com/posts/a-successful-git-branching-model/

Atlassian's SourceTree also helps us with maintaining "the flow":

http://www.sourcetreeapp.com

https://www.atlassian.com/git/workflows

Git extensions and screencast on how to setup on OSX:

https://github.com/nvie/gitflow

http://build-podcast.com/git-flow/