Topic title explains it. I don't think it used to be this way.
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This has been a thing since D1. I used to set myself to show as offline regularly, when I just wanted to do my own thing, but I would show as online in-game when playing Destiny. It also can occur in other online games, depending on how the devs have things setup.
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The companion app will show you as online, appearing offline is a platform setting only.