Well that doesn't make any sense to me. First of all, I don't believe that "punk" thing that they are not about selling records or being popular, any band does music for a lot of people to listen to it and to go to see them live, otherwise they would just record their music for themselves. If a band becomes popular, it's not a bad thing, it's actually a good thing, specially if they're punk, considering how hard it is for that to happen. But ok, it's something I can live with, Punk is not a genre that can be regarded as one of much popularity so it's ok in that way.
Initially punk attitude was very much about not selling many records but rather appealing to a small subculture only. Soon punk entered the mainstream and you're right that mainstream popularity probably should be acknowledged as well. But as the criteria currently stand it isn't taken into consideration.
Second, what is a pure punk band? Ramones were punk-pop if not pop at all. The Clash? You know, that band that is in the top of this list, how are they pure punk? If there is something about them that makes them different from most other punk bands is that they tried new sounds. How is London Calling (One of the best albums ever) pure punk? It isn't. There is a broader spectrum of punk. Green Day makes Punk Rock music. Not straight punk, sure, but they have quite a lot of the characteristics of a punk band. How can there be any innovation if there is something called "pure punk" and no one is allowed to go outside of that without being considered "not punk"?
Ramones were pretty much the first true punk band. Later they became poppier but in their early years they were pure punk. The Clash similarly started out as a pure punk band. By 1979 they'd begun experimenting with other styles as well, but their debut album is as straightforward as punk gets. Green Day were pretty close to alt-rock right from the beginning.
One of their albums created a musical in Broadway. Now a movie will be done about it.
By the current criteria this is irrelevant.
They are one of the few bands nowadays that puts good guitar music into the mainstream with success (that also has political content).
The first part is completely subjective, the second one is irrelevant.
They have influenced a whole new generation of bands (doesn't matter if you like them or not, they did it). That is influence and innovation.
That's true. It's propbably why they're as high as #19.
Sure, they're not very popular with hardcore fans because most people have the impression that they "sold out". But they didn't. They just changed, which is the obvious step for any band that has 10+ years of history. You can't pretend for a band to be the same for ever.
This again is irrelevant.