Weird, I got git 2.6.1 using the same command:
$ brew install git
==> Downloading https://homebrew.bintray.com/bottles/git-2.6.1.el_capitan.bo...
$ git version
git version 2.6.1
$ brew upgrade git
Error: git 2.6.1 already installed
$ brew install git
==> Downloading https://homebrew.bintray.com/bottles/git-2.6.1.el_capitan.bo...
$ git version
git version 2.6.1
$ brew upgrade git
Error: git 2.6.1 already installed
brew update
brew upgrade git