Yeah – basically all git operations are done on a clone of the repo. This is a “good thing” – it means you are not tied to good internet for ability to work.
Of course, you don’t have to clone the whole repo – you can, if you choose, do a “shallow clone” only containing the history of the branch you select. Maybe this is what you were thinking of?
There are situations where you want to work on a repo without checking it out and even that is possible via such online tools as http://prose.io (I’m not an expert on that, tbh, just heard about it) or use some of the web editing tools built into things like GitHub.
Rachel