Have you tried GitX? What you described seems a bit more like GitX than what GitHub is trying to do here.
When I first fired this up, I made a tarball of one of the repos I'm currently working in (it has uncommitted changes) and started clicking around. I'd do something in the GitHub app, then go back to my bash prompt to see what happened. I was pretty confused when I switched branches and all my changes were gone. Then I went back and read the blog post. It auto-stashes when you switch branches. I also wondered what the heck the "Synchronize" button does, so once again, I referred to the blog post. It performs what they call a "smarter version of pull --rebase && push that reduces merge commits but doesn't rewrite your merges". Oh, really?
At that point I realized that GitHub has done the hard thing. They haven't re-created the git CLI tool in a GUI, they've created something different. They've created a tool that makes Git more accessible. Little things like auto-stashing when you switch branches will confuse git veterans, but it will make Git much easier to grok for newcomers because of the assumptions it makes about your git workflow.
I see great things in this app's future. It's probably not for everyone. If you're a proficient git cli user, and you like it that way, then you're probably best off sticking with what you've got. Maybe explore some of the more traditional Git GUI clients like GitK or GitX, but keep in mind, that's not what this is.