Firstly, was Simon actually in Adventure in the US version? I found a magazine ad for it once and posted it on the dungeon, but I figured it was a very early ad and they had assumed it was Simon or just said so to sell the game. Does the US manual say it's Simon?
A magazine with important ties to Konami (not just "some magazine") and even the advertisement itself say it's a completely new game. What more evidence do you need? You can't just dismiss this because in your opinion the game looks like a Castlevania game and therefore it must always have been a Castlevania game.
He's saying that aside from the Morris clan having been descended from Belmonts - which Shinobi's post backs up - there are certain things in the game (beyond key gameplay elements like candles and whipping) such as the first level of Bloodlines being the first level (and ruins) of Castlevania 1 - up until the room with the werewolf. This is probably the biggest one in my eyes. It's difficult to ignore things of this manner as they infer continuity. If I'm understanding Alex correctly, if I'm not he can correct me. (that rhymes)
I think there are a lot of semantics going on here though. So I can't read Japanese but let's assume the game was a Gaiden, intended as spin-off series. So it's a gaiden, intended as a different series
in Japan but looks like Castlevania, plays like Castlevania.... If it looks like... (I know there's a joke about the graveyard duck in here somewhere).
In the end I'm not really seeing what the punch line is. I understand Nagumo's evidence, but I hear what Alex is saying. I find myself indifferent and can only think that for example if tomorrow Nintendo states in its own Direct that Super Luigi U is no longer canon to the Mario series, then it's not. However, it seems so specific and trivial given the games key elements, gameplay aesthetics and how the game feels, would anyone be paying attention to this? People are inclined to believe things by experience is what I'm trying to say. I would've welcomed a series of games with the Bloodlines feel. So even if it was intended in X way, it's been taken as Y by the most of us. It's not something I personally view as problematic. (Hell, a lot of people don't even consider Curse of Darkness to be canon to Castlevania.)
If it was a spin-off series but based in the same universe AFTER the original CV series, that makes more sense to me given John Morris walks through the original Castlevania's ruins in the first level.