You said they altered the gamertag system. Is that such a good idea? What if I accidentally leave my console running at home, and I want to sign-in at someone else's house? What if I have my profile at someone else's house, I'm on at my house, and he tries to sign-in to my account (be it accidentally, maliciously, or just to mess with me)? Will it kick the first sign-in off, completely deny the second, or (what I would assume) require password verification?
Sorry, I now realize what I said was confusing.
In the Fall 2011 Xbox 360 update, they overhauled the gamertag recovery system. It works a helluva lot better than it used to. I'll explain how it works, as I've used it plenty of times.
You can have your gamertag "recovered" on an unlimited number of consoles now, all at the same time, without invalidating any of the others. If you leave your console running at home and go to sign-in somewhere else (whether you need to recover it, or your gamertag was previously recovered there) then there is no problem. Just pick up and play. It will sign you out on your home console. At any time, from any console (and xbox.com), you can choose to "lock" the gamertags recovered on every other console with your account password.
I went to Canada and recovered my gamertag on my cousin's console. I was unaware of how the new system worked in regards to multiple sign ins. I had told my roommate back in the US that she could use my Xbox to watch movies on my Netflix account or via DVD or whatever while I was gone. In the middle of a game in Canada, I get the "Your gamertag has been signed in on another console" pop up (looks like an achievement notification) and was signed out of Live. I hit the guide button and signed back in. Then it did it again, 5 minutes later. This back and forth went on for awhile, until I figured it out and called my roommate, who was confused and figured she wasn't doing things right since it kept signing her out of Netflix. I think she was constantly powering on and off my system at home, since she has no idea how to re-connect. This is when I discovered the option to require a password on all other consoles (alternate option: all consoles, including the one you're on now). You do have the option to never use it, and keep everything password free. When you recover your gamertag, it will ask if you want to password protect it anyway, but even if you forget to do so - you have remote options.
When I left Canada, I used that option to basically "nuke" my gamertag from my friend's system. I forgot to delete it before I left, but if it requires a password, he won't even be able to accidentally sign in - and I'm sure he's deleted it by now anyway.
And that's how it works on the 360 right now. True story.