Apparently, according to Marc Whitten (Chief Xbox One Platform Architect) you can plug the HDMI cable of a 360 into the HDMI IN socket on the back of a ONE and plug another HDMI cable from the ONE's HDMI OUT socket into one of the HDMI ports on the back of your HD TV and more significantly, seamlessly use both with no impediment. You don't need a second account and as ONE is wireless you don't need a free router socket.
"'You’ll be able to be signed on with the same gamertag on both an Xbox 360 and an Xbox One console at the same time...However, like today, you can only be signed into one Xbox 360 and one Xbox One at a time.'"
I genuinely wasn't aware of this and mistakenly thought that I would have to Sign out / Sign in when switching to play Halo 3, etc. which I'm still going to be doing on a regular basis well into the next-generation as it is so amazingly perfect.