as much legitimacy as

[Irelia20150604]

Hi everyone! I'm not sure the meaning of the phase "“And these guys have just as much legitimacy as anyone else". Does it mean "Like anyone else, these guys (ISIS members) are also legitimate Muslims (Conformable to Koranic)" ?

the context is as follows:
===
"... As if there is such a thing as ‘Islam’! It’s what Muslims do, and how they interpret their texts.” Those texts are shared by all Sunni Muslims, not just the Islamic State. “And these guys have just as much legitimacy as anyone else.”

Source: http://www.theatlantic.com/features/archive/2015/02/what-isis-really-wants/384980/

 

[Glasguensis]

I believe that what is intended here is the following:
The interpretation of the ISIS members of the text is as legitimate as the interpretation of any other Muslim.

 

[Irelia20150604]

Thank you, I get it. Without your explanation, I think I would never understand it.