No they do not have any points to back themselves up as the "Greatest band ever.".
There are reasons you may think they are, but no matter how many people think it, it's never any closer to being a true claim.
Britney Spears caters to the musical preference of the masses, it means absolutely nothing. The Beatles were a great band, and that's all they were, in my opinion. There were great bands before, there have been great bands since, and in my opinion; Better bands before and since.
You disagree, so do many, but that essentially means nothing.
They have a lot of record sales, the innovated a few things, so what? They get credit they don't deserve, and the influence thing is just an estimation. Massively influential? Sure. How influential is that? Nobody knows, but people like to think it applies to EVERY music fan and EVERY band.
They are overrated.
-AC