I would think you do not have Youtube Live. The Live Broadcaster template seems to be showing up to all Youtube users whose account is linked to Google+ and in good standing. This is because Hangouts on Air (which is now public to everyone) can be simultaneously broadcasted to our youtube channels when streaming live (if that template is selected). I have the template too and I confirmed myself that is what it is for. Youtube/Google isn't exactly the greatest in keeping up with their support documents as you probably are well aware.
Also note, if you are partnered with a network (AKA Fullscreen), then the network as a whole has to be invited to live stream, not the individual. This is because Youtube Live is still tied with Content Manager (CMS) accounts, which only the network adminisrator would have. I would imagine the network would make an announcement to its partners when they can enable livestreaming once they have it.
In the meantime, users can always use Google+'s Hangouts on Air.