So I was saying that Android runs the Linux kernel, period.

But now that you say it, Android is very much a full OS. It's not a Linux Desktop, but it is a full OS. And televisions running Android are called "smart TVs", precisely because they run a full OS instead of a minimal firmware like they used to.

Google is working on bringing Android to the Desktop, and Samsung already does it. As in: you plug your smartphone into a docking station and it is suddenly a Desktop computer.