I am the one that agree with the statement "there are particular agile methodology inside adopted software development methodology". In fact the term agile is commonly used, but it could be applied on one of software development methodologies that popular currently.
I found and experienced while adopting one of them, I have been used Iterative methods such as RUP with adjustment on specific company's software process, and there we are still need particular agile implementation inside as specified as agile methodology is "light-weight methodology" to gain lighter, faster and more people centric approach.
Practically we have to make the software requirements, software design, software testing and project time management as well as communication should be more agile instead of applying the whole adopted software development process as is.
Conclusion, we can apply "case by case" methods to meet our need during software development process. The one that good for us should be comfort to be followed by the team member, as well as the stakeholders.