Regin himself is rather shady—what with egging on his charge to kill a ferocious dragon no one has ever even attempted to fight and staying at a safe distance as he does so—but shadiness isn't quite the same as villainy. In all other instances, he's supportive of his foster-son and scarcely mentions the gold after telling his story. He very well could have just been really concerned with vengeance and gaining power from Fafnir's heart, but felt ambivalent about the deed after it was done ("You killed my brother, but I can scarcely be free of blame for the deed"). Fafnir's taunt that Regin did want to kill Sigurd was possibly just that—a taunt.
Also, Sigurd gained the ability to understand birds' language from consuming Fafnir's blood. Fafnir, who after being transformed into a dragon became as cursed as the treasure he made off with.
Perhaps the birds that warned Sigurd about Regin really were talking to him, but consuming Fafnir's blood induced a drop of madness in his psyche, leading him to warp their message in a way that would justify killing his foster-father and taking all the gold for himself... just as Fafnir did, after killing his father, Hreidmar. It was only a drop though, so the curse didn't affect him anywhere near as drastically as it did Fafnir.