Having a Microsoft Account (Live) and having Administrative Rights on a PC is completely two different things.
All the Live account does is allow you to use Microsoft’s on-line services. Once you establish a Live account, you can use it to sign in for various services such as x-box, E-mail, the Apps Store, SkyDrive, etc.
Under Windows 8, it allows you to use your Live account as your main Profile, which also provides uninterrupted service and connection to your other Live services you may be using. It has nothing to do whether you have Admin rights or not.
BTW bear in mind that you don’t have to have a Live account to use Windows 8 (Local Account - Switch to in Windows 8), it just make it (Win 8) easier to use if you do. The whole thing about Win 8 is it’s a "live" experience.
That said, if the PC belongs to you, you should have full rights. If not, you shouldn’t be installing anything on it without permission from the owner anyway.