Gonna put one of my thoughts in a spoiler tag to be safe, 'cause not everyone wants to read speculation.

Also, technically, a Game of Thrones spoiler/reference.
I'm not convinced that Joshua was actually the Archduke's son. After watching the scene with Joshua's/Clive's mom that follows the combat tutorial, I immediately thought that Joshua was Murdoch's son instead. To be fair, though, I think this, in part, because FFXVI is channeling Game of Thrones so hard.

Maybe Joshua has strawberry-blonde locks (unlike both of his parents) because he's the Phoenix, but it's hard not to think there's more to it.