Git auto-completion not working on Mac OSX 10.11.5 El Capitan
You are confusing the basic bash completion with the add on required for completing git commands.
The git that is installed by Apple lacks the required git-completion.bash file so you need to install the full git. You can do this easily with homebrew -brew install git will do the job.
Once you've done that then uncomment your top three lines :-
if [ -f $(brew --prefix)/etc/bash_completion ]; then
    . $(brew --prefix)/etc/bash_completion
fi

Now source ~/.bash_profile and it should work fine.