I disagree with both of your statements. Hypergrowth is a meaningless term and a startup is a type of company in a specific stage of its lifecycle. Running a company "like a startup" can be a thing, but that does not make the company a startup.
Based on my experience at Amazon, I believe this is something you hear at megacorps that are in denial about their current operating procedures and also don't understand how a startup operates.
Startup is also a way of running a company, not just “young company”