No, you're unfortunately not correct in your understanding. Yes, "agile" is an adjective that means "able to move quickly and easily." "Agile" is a proper name and an umbrella term for product development approaches outline in the Manifesto to focus on responsiveness and ability to respond to change. There are plenty of Agile Methodologies, Frameworks, Process, Practices, etc. Scrum is very much an Agile Framework and therefore is Agile. It is also not prescriptive, it's the exact opposite. Anyone discussing Big-A and Little-A in the Agile space just has never achieved beyond a pre-101 level of understanding. I would encourage you to study the content in Scrum.org and Agile Alliance to move beyond your current misunderstanding of Agile, you won't need consultants to do so. Good Luck!