No it's not suplex. I'm 100% sure that it's the Izuna Drop and no matter which FAQ and which fanboy tells you it's suplex, it's not. I know this because it is the throw associated with ninjas and every ninja in every video game uses it, whether they are Spanish Ninjas or some other ninja. It's actually a cliche for ninjas. I can give you a whole list of ninjas that use this move and you can go see for yourself.
I never checked any FAQ or fancy whatever - I just played a lot of SSB and Kirby Superstar back in the day. I did just watch a youtube video of Suplex Kirby, and he did the move from SSB.
...wait....I think we're talking about two different throws here. Kirby's back throw is definately from Suplex Kirby.
(I can't see the dojo from work, it's blocked. So if this throw discussion started from something seen on the dojo, I wouldn't know about it.)