So, earlier today I noticed that my Nexus 5 running Android was saying “No account is currently storing backed up data” in the Settings -> Backup & reset menu. Having searched on Google for a solution, most everything I’ve come across recommends force stopping various services on the device or doing a factory reset.

Well, if you get this problem, do not do either of those things. Simply remove all of your Google Accounts (Settings -> Accounts -> Google) until no Google accounts remain, then restart your device. When it reboots it should complain that you have no backup account. Sign into your Google account and voilà, problem solved and without the painful data loss you might suffer with a factory reset.