You know, they could also have called him Simon Belmont VII. Or say that the protagonist was named after Simon Belmont or whatever. So, I think that argument is a little weak.
To expand on why I think Castlevania IV was meant to be a reboot, when the game was a released, a guidebook was released called "All About Akumajo Dracula". It's a very interesting guidebook because it expands on the storyline of the game and pretty much ignores the games that came before it. For example, the guidebook says that the Belmont Clan is not an actual family, but a clan of Dhampirs.
Secondly, when I had that talk with IGA he told me he considers Castlevania IV to be an alternate continuity. So, I think the common assumption that this game is a "remake" is false. The only game that has been confirmed to be a remake (in the loose sense of the word) is Akumajo Dracula X68000, and even that game is described as a "rearrangement" of the original game.