When they say "you can't separate" the two, that's absolutely not in reference to sidechains or other similar schemes.
Quote from: Sidechains white paper
In this paper, we argue that it is possible to simultaneously achieve these seemingly contradictory goals. The core observation is that
Bitcoin the blockchain is conceptually independent from bitcoin the asset
Bitcoin the blockchain is conceptually independent from bitcoin the asset
I was referring to the meme the guys in the video were addressing.
Mainstream meme : You don't need bitcoin to use Blockchain technology.
Blockstream : You can move Bitcoin around to other chains.