Well, it isn't a debut. They kept the same name, so it's the same band who released the previous 2 albums. It would be like saying the new Underoath album is their debut because they don't have any original members.
It doesn't make any sense to me saying that you call Fake History their debut just because you don't like their earlier albums.
was their first album that received any notoriety, their first one with a publicist, their first one with a reputable record label, their first one with their current members, and the first one anyone heard of. It's their first time trying this sound. Jason was known in LA, but nowhere else; I live less than 60 miles from them and I had never heard of them til their latest. So no, technically it's not a debut; it just has all the qualities of a debut.
But, I'm pretty sure we all refer to ...Is A Real Boy
as Say Anything's debut, even though there are several albums that pre-date it.