I don't believe that's true. That's why you needed to be able to
transfer licenses from one console to another.
For example I have DLC for Rock Band that I downloaded on a different console than the one I have now and I can't play those songs unless I'm online. Any songs I purchased on my current console I can't play without being connected to Live because they are licensed to that physical console.
With the Xbox One
it works differently, all purchases are tied to your gamer tag only.
So even though I tend to purchase my games on my living room console my bedroom machine can immediately download all those games even if I'm logged in on that machine and even if that machine isn't connected to the internet. Plus I can easily switch my home console to another machine without having to request a license transfer. I can do this 3 times per 365 days.