He may have you on "hide conversation". I checked this multiple times with my friends and that's exactly what it looks like. Facebook as a piece of code receives conflicting signals, because it knows it's supposed to show this user "offline", as he hid you, but the site can't relate to the time when he supposedly left - because he didn't - so it shows "online 1 minute ago" as a compromise.
Facebook deals very well with inactive users and, if you don't use it for some time, it will automatically render you offline. I often have this problem with my boyfriend, because we see each other offline even when we are in the same room, both obviously online - but it shows otherwise when we switch tabs to something else, despite keeping Facebook open.
In general, Facebook does a ton of lying and errors about statuses. So your bf might be telling the truth about leaving the phone on. But if these naps happen too often and at weird times, he's simply hiding you from his chat. Whatever the reason.