Totally. I was trying to explain how the concepts and people fit together, to give some context to the tools and approaches we have to choose from.
To your point more directly, I'm of the mindset that you can "do Lean Startup" without explicitly subscribing to it as a methodology. My goal is to help people understand the underlying concepts to see which approaches make the most sense for them, and even to the point where they can adapt them and come up with their own ways.
One of my favourite serial entrepreneurs, Nick Imrie, once told me: "We used to do Lean Startup. We just called it getting experience."